History of Values of Ramanujan's signature hypergeometric functions $F_r(x)$

 Display properties:   number-header: $F_r(x)$-Numbers: []+Numbers:+- params:+    r: '2'+    x: 1/2+  number: '1.180340599016096226045337940558488587233716634881447299515864399404304180720715794978458616195807954'+  comment: A Gauss second-summation value, equal to $2/B((r+1)/(2r),(2r-1)/(2r))$.+- params:+    r: '3'+    x: 1/2+  number: '1.159595266963928365769992051570020881945165263439782855263105059747973757205286258658085251051146071'+  comment: A Gauss second-summation value, equal to $2/B((r+1)/(2r),(2r-1)/(2r))$.+- params:+    r: '4'+    x: 1/2+  number: '1.133915559726082732440156510347438791344295356805403611236317061400497913023777214458207113170347034'+  comment: A Gauss second-summation value, equal to $2/B((r+1)/(2r),(2r-1)/(2r))$.+- params:+    r: '6'+    x: 1/2+  number: '1.098430696839862068942935161608698822283938481692253723027033945469518521905843821564973446230505442'+  comment: A Gauss second-summation value, equal to $2/B((r+1)/(2r),(2r-1)/(2r))$.+- params:+    r: '2'+    x: 1/3+  number: '1.103845772797212254324837694207631411924760802239391086997330526905118375631119575423168443314817465'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/3+  number: '1.092060148081664394316757805253605515050933694436801793669960490099214146997645089823341657245948803'+- params:+    r: '4'+    x: 1/3+  number: '1.077415715750701203246257098513742012348092021182187093026426589300763704600445579059592620512413547'+- params:+    r: '6'+    x: 1/3+  number: '1.057076261613892128402122962965324995470501889069986725795375244685741777798779952700216143078965700'+- params:+    r: '2'+    x: 2/3+  number: '1.291675482135082644544318504760649923199863516052326580950539239585172786733440152066839813967604411'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/3+  number: '1.257546863411625467745864646361554193208060216425676017110925090768116861297340574645820318884594719'+- params:+    r: '4'+    x: 2/3+  number: '1.215502554868454386941982217997043941288277531484048915816265650173538426379192234806255033882957850'+- params:+    r: '6'+    x: 2/3+  number: '1.157778216364893874950561674893505207806365917352306655090978043246823064194951989915747252390826364'+- params:+    r: '2'+    x: 1/4+  number: '1.073182007149364375052841707970349795669526818631368625787232257139788343028625222768722717743272285'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/4+  number: '1.064925231128516498437819437604916718248282322874928859475392443772515623080612622146534197451821389'+  comment: $1/\mathrm{AGM}_3(1,(1-x)^{1/3})$.+- params:+    r: '4'+    x: 1/4+  number: '1.054648614831467047906718149577441840630273364763410414893082861937658163667864603886693740230931228'+- params:+    r: '6'+    x: 1/4+  number: '1.040343865043574145416878113346879640594465685268916549682386133655136588848837323908014059028010148'+- params:+    r: '2'+    x: 3/4+  number: '1.372880500618350164697637575007806058094538625348940055855540038870350633240892464904292347403572711'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/4+  number: '1.328778200157056363878073355047905281137317875982473604891262407713582251790491637816553512224526597'+- params:+    r: '4'+    x: 3/4+  number: '1.274611308136601952102809952021133623397842247250675660982363975799881719700368808191505969508039952'+- params:+    r: '6'+    x: 3/4+  number: '1.200547022551705970623606133782633712417243715140519123069736520860927175815592908672157063181494441'+- params:+    r: '2'+    x: 1/5+  number: '1.056549197563300524078647664524631546162020827872518214905496804039471255692357951593748576322171397'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/5+  number: '1.050190162034047216423273458755210265735253912697437725038968163649388321021812855122591150688006205'+- params:+    r: '4'+    x: 1/5+  number: '1.042268132787808640280111359191757076616454207746347141456642938948577695890045478200055253124276725'+- params:+    r: '6'+    x: 1/5+  number: '1.031227120754513755409097443523206049076896713820691129797578601885727886494785009328601926518885676'+- params:+    r: '2'+    x: 2/5+  number: '1.131603977657727948718251611721629596963366772407109106123290929200991062332448898357341008018769227'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/5+  number: '1.116591847517491603078398227585544469068273798398588049562491365127247729007411521979714563385367573'+- params:+    r: '4'+    x: 2/5+  number: '1.097964954833625034644635115029838609229817266028104295629106404832222814579922722381761885136262909'+- params:+    r: '6'+    x: 2/5+  number: '1.072143911441301239285308516371365056707681862588226702509208055792540419288310570835512134058490225'+- params:+    r: '2'+    x: 3/5+  number: '1.241133377096689973536682961615741508733165956734589222952496929906656479540528590897435022372835882'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/5+  number: '1.213125929265749290045665105498391869491955138301218750013311846419003653696516756626615190713296483'+- params:+    r: '4'+    x: 3/5+  number: '1.178550802124159000837858875238875243852949017127044523005083344491627440708876190233450341698228100'+- params:+    r: '6'+    x: 3/5+  number: '1.130948205380449462465758079793859332992924379485001810147213340696353596026888283755154647046083428'+- params:+    r: '2'+    x: 4/5+  number: '1.436981541347583904374530510658727657178127808659478463032740900956857996992894943971118927044229213'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 4/5+  number: '1.384900768403713295980836955613618765996932275485885300036548344312948779899235384765120985000191027'+- params:+    r: '4'+    x: 4/5+  number: '1.321072304137970981489625469511684229549308657735090684183580728605552210350786647000383877823149081'+- params:+    r: '6'+    x: 4/5+  number: '1.234051513166650938678727539689680863939511554700611297922727915011535080521962974286976418925727248'+- params:+    r: '2'+    x: 1/6+  number: '1.046091783138450905722887670068762559303746574800383734428214108534602441219885573271726413888274227'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/6+  number: '1.040919744138056218742701069892397123860878861236686382807648423603974286719266533999771862365356725'+- params:+    r: '4'+    x: 1/6+  number: '1.034472595975224665565210956965449694286788213307133302690146790981876687220797791144859155481474093'+- params:+    r: '6'+    x: 1/6+  number: '1.025479929962698069513640244088735839728532206675693532543652327980646441501018133834688540007781577'+- params:+    r: '2'+    x: 5/6+  number: '1.490006710996101632048041757023586658936775098622123546456694903920849499466878439839757245006245228'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/6+  number: '1.431264829472441829703947649619931413395224683882458059073668339881763624192223392310901044689123357'+- params:+    r: '4'+    x: 5/6+  number: '1.359390804098473584376788492257887972976230618168990794668557788882956618905982520170923667645410207'+- params:+    r: '6'+    x: 5/6+  number: '1.261618848974220823232875404352187310613282634782723761417481556764687432263870744040189009223890045'+- params:+    r: '2'+    x: 1/7+  number: '1.038904133044564197904811634148864850543294789667688054067546601491881507649076613798838908792871211'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/7+  number: '1.034545122849013258464320235923431824838519691492821668016344638509330279300214298221229219460208758'+- params:+    r: '4'+    x: 1/7+  number: '1.029109172003885640883409790532973787966389722225236362612312609792303595339076362320466658371673082'+- params:+    r: '6'+    x: 1/7+  number: '1.021522711978899270161484565462790266324217042630435591158386825263565261340839493875442725470508843'+- params:+    r: '2'+    x: 2/7+  number: '1.085836219042230225420359741943770555185613239379711403618484105693628970552675777371878731716489871'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/7+  number: '1.076127821155113612750818858776430927664391876945783155757827903850477326425261991200767457088468650'+- params:+    r: '4'+    x: 2/7+  number: '1.064052855706798065059318519246029202243427610149994583873678689162568557377211969188254443666791935'+- params:+    r: '6'+    x: 2/7+  number: '1.047260452636646291936905526288772566333611423555714912707320878408599967268426922402365851159317897'+- params:+    r: '2'+    x: 3/7+  number: '1.144560363318554196151258236386538674584153252036171984443250885612698680823735943280588129450616996'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/7+  number: '1.128032332151065543728238163703959988069884239240462769722960859006034030405693314087008682285193629'+- params:+    r: '4'+    x: 3/7+  number: '1.107537793322367653266005014370961059569233422517096275050673312685427899341636698533315407572250209'+- params:+    r: '6'+    x: 3/7+  number: '1.079152424402878754693764677906191997647926816101214401332204094757707475494039972314185499830646974'+- params:+    r: '2'+    x: 4/7+  number: '1.222207887117855933150549202510695161112895220266936745908836236619192022096820532314266970327331576'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 4/7+  number: '1.196473564871515518228785425183390940789314777619902920985397928655142565693070797494023465587804910'+- params:+    r: '4'+    x: 4/7+  number: '1.164678584288915160597719744440372368619041696755789177096439287888089589762692865574694327714695891'+- params:+    r: '6'+    x: 4/7+  number: '1.120855392722023755059851942906939798671290619276856034395792254830210759062760167632958693523784511'+- params:+    r: '2'+    x: 5/7+  number: '1.334976602403716770127827025536283176651684589423227647458068504567674708882393623447928128047799559'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/7+  number: '1.295549635583874100749921062420089511310885550300578971974390063341866749753562644478408989657098971'+- params:+    r: '4'+    x: 5/7+  number: '1.247058654519720467529444007209479917722934199631468498536085139193313512364032380250987836581499310'+- params:+    r: '6'+    x: 5/7+  number: '1.180632392947737505509653963634824163140583810153045236078522693791175570750097421002180002810962377'+- params:+    r: '2'+    x: 6/7+  number: '1.535256663440011474732454706314617512498973195528800109170420969834694307748934528735174488793888015'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 6/7+  number: '1.470791296583444910638740268211626314580220190451585807085004608970441862434825710374791292919191265'+- params:+    r: '4'+    x: 6/7+  number: '1.392017425082818827052250945693554995149461510680459772868971988838488279020453270175854537750954101'+- params:+    r: '6'+    x: 6/7+  number: '1.285049626185067519149090613022787767841242600927099986053399274274054232969578961964855661848821311'+- params:+    r: '2'+    x: 1/8+  number: '1.033658320257222080650660793407819301371959086449491349266378925511332812850157652680195437582610948'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/8+  number: '1.029891211707070937723394681657891254219688227846421021674796234582582177220985558207517716686222714'+- params:+    r: '4'+    x: 1/8+  number: '1.025191948147477204555870898040341068871121508224311888461749724469665489111473743828715077692710259'+- params:+    r: '6'+    x: 1/8+  number: '1.018630911495653293538424281488276717631384100968154539202986813100150927326279908118200895782928464'+- params:+    r: '2'+    x: 3/8+  number: '1.120812916187724835510613192799134646059099550620059458865703824388030737774532390034712889934777390'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/8+  number: '1.107058591834453422500498838406624759570443201432808670785993628303478823787075589877961046097012653'+- params:+    r: '4'+    x: 3/8+  number: '1.089982996436349562230291086266379866968836215243603630021467036634028291166639603728674550705978222'+- params:+    r: '6'+    x: 3/8+  number: '1.066294964728936761384711034263120630667179508266381417209665290649859741745557242745148953209219164'+- params:+    r: '2'+    x: 5/8+  number: '1.258938040853862956996168399328334822946195216227027907564484731201390225011645978979010358952157225'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/8+  number: '1.228782449126488018539047223851035872614005142163756355285504314300773493210125954143540802655757776'+- params:+    r: '4'+    x: 5/8+  number: '1.191583327892024549438019833834561300225000412141646104404464790759077035010424432025608253740841480'+- params:+    r: '6'+    x: 5/8+  number: '1.140419707762858011965213197113139193077077612250061736334808692654418410558010581934796829539301298'+- params:+    r: '2'+    x: 7/8+  number: '1.574740233062900749709511580466414225965172203836240246998315913582919707616074949971864542148614141'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/8+  number: '1.505254038857066011299767910248401498208259856931645808635186143997248989499343595330290706097970142'+- params:+    r: '4'+    x: 7/8+  number: '1.420436405603149035164429103674611486604556948768265300039881213202036094679225782024480005713671310'+- params:+    r: '6'+    x: 7/8+  number: '1.305430277962542151058027584538875267811926497386817849305164939127018945600601626244266404389366698'+- params:+    r: '2'+    x: 1/9+  number: '1.029660375463762623523228181255854543570903969011705041891655029152762974930669348678219260552679533'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/9+  number: '1.026343520841566885711818335651046428274180826014178666730958109479707060905841596720020526615780503'+- params:+    r: '4'+    x: 1/9+  number: '1.022204943866080919860161806857062989134020137789994880270437701856939901361339037391092749731504665'+- params:+    r: '6'+    x: 1/9+  number: '1.016424899916147157209316669882466843802873309665909634999036140962440390965478130838565284637450640'+- params:+    r: '2'+    x: 2/9+  number: '1.063794415811677049552541647164834182538425445440191871843236008928428344208836477382503166338992521'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/9+  number: '1.056610187209305634509752575084449105338086804837491860759765218539835253267529709258419364649947724'+- params:+    r: '4'+    x: 2/9+  number: '1.047663807509503253763962332160564725355600096306203016834789709390477727619762834985644836709259122'+- params:+    r: '6'+    x: 2/9+  number: '1.035201978727051510335924015685416579908386169806777936956330730944242498718418183220770658796796304'+- params:+    r: '2'+    x: 4/9+  number: '1.152070109037683005025037166134955830569733070726355371852509034427494430837553305319982903163462641'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 4/9+  number: '1.134660648114355403631337399466476138628544423535191018086134518681213796429802162682889092477494993'+- params:+    r: '4'+    x: 4/9+  number: '1.113081115689331418869325768112246824537379728332091716607837515961784678747445039488847502084758853'+- params:+    r: '6'+    x: 4/9+  number: '1.083207808460837506949863035558834733529058098651934955323580947078361815258019125807530880050500963'+- params:+    r: '2'+    x: 5/9+  number: '1.212277737388446126114849206956631294516399256257202991733337430972124890082201154989536831079765176'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/9+  number: '1.187731753381443821101320706625882493021599661502139327862103330238600432166839150503617694239926203'+- params:+    r: '4'+    x: 5/9+  number: '1.157391657238803968433859244888091901309236348718160614407357508950030616405857074098800775120177135'+- params:+    r: '6'+    x: 5/9+  number: '1.115549034672973546023540352121884997137378434959801726832217629491907774083435314436783779577798586'+- params:+    r: '2'+    x: 7/9+  number: '1.406601154881691402593472192886194359659700508109655428310351240159337356982388830048124345702344339'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/9+  number: '1.358312435705690357986949710962349877080998310068052564784840695120381752100133197132806489600122829'+- params:+    r: '4'+    x: 7/9+  number: '1.299072366877585719463141430187516699409725288457885838899818923753290643107951245283574655396808381'+- params:+    r: '6'+    x: 7/9+  number: '1.218198107849993176657400023408565088498766778634250505932396191626566673931547758165831938143491085'+- params:+    r: '2'+    x: 8/9+  number: '1.609773010724046562579262561955524693504290227947052938680848385709682514542937834153084076614908428'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 8/9+  number: '1.535812809958194137289311853725147146475663454326775827621496728753103561572492083134212409167445065'+- params:+    r: '4'+    x: 8/9+  number: '1.445616095140239952072718914467638749495268402565399677644614166992051212768192453714749044140042691'+- params:+    r: '6'+    x: 8/9+  number: '1.323467526740777845709483066819782686939481648265356144701869051624955722200944233060569225543086875'+- params:+    r: '2'+    x: 1/10+  number: '1.026512044378341921684211979827646737352861418956689804570238131348948968554188533262148256466594475'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/10+  number: '1.023549238829423071188169685444329193566581063931538749518423631994710790474632618839510169768428974'+- params:+    r: '4'+    x: 1/10+  number: '1.019851729415091843526358207816823199616111797408573908950154741278999619171876569877757774802125548'+- params:+    r: '6'+    x: 1/10+  number: '1.014686397293902488848773808132326995460963389822135686318875401550751735397643971017161747167955139'+- params:+    r: '2'+    x: 3/10+  number: '1.091095910362781566395412210019548535491316580086392618691450030536134538831405356974682221464949521'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/10+  number: '1.080782209186556170155428610341809305181042107791418949037651214294649120395376910063142833674184175'+- params:+    r: '4'+    x: 3/10+  number: '1.067958034329354309181998720508432373228618500815506410559014146863362839020747504379185686844154080'+- params:+    r: '6'+    x: 3/10+  number: '1.050130505525393752543392435286971744933842913117885616261354068552253289500531337208548127076474095'+- params:+    r: '2'+    x: 7/10+  number: '1.321217206769961628317271699220734673082433136489992485826932636346228350095608636981900391995144021'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/10+  number: '1.283478964116754298216757307564906253314665492204852243043222340743204179162304530348183365772283111'+- params:+    r: '4'+    x: 7/10+  number: '1.237040972195965067507214627505413280493090366952305815886395676403567796300574398662733422049912894'+- params:+    r: '6'+    x: 7/10+  number: '1.173382687647331618877433037707868835889088566992027544770349319783019806813872106817231525040982274'+- params:+    r: '2'+    x: 9/10+  number: '1.641264414342370733286999747367830456947182410886698750765421537225059699558810851709768888498397108'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 9/10+  number: '1.563268212972069953487391346705679048399059802492935756214049227368641731628039675849038738599696945'+  comment: $1/\mathrm{AGM}_3(1,(1-x)^{1/3})$.+- params:+    r: '4'+    x: 9/10+  number: '1.468223828302126866617020254556201986284671438655060147322921731084641754120807497000027340805666758'+- params:+    r: '6'+    x: 9/10+  number: '1.339647244892691643646577789238076526892547089442876234566511576888432612311421152714764190141793242'+- params:+    r: '2'+    x: 1/11+  number: '1.023968347371686311918078592385397263566137880870782763162684166767298617336501277303748294085862560'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/11+  number: '1.021291258951993964175132732967530845368701631760419883631073286468895655282506451238914602282882422'+- params:+    r: '4'+    x: 1/11+  number: '1.017949808347388069925036572359200727407752788316734278788094849366293932486562079862224350120127926'+- params:+    r: '6'+    x: 1/11+  number: '1.013280932066269384409544564443784330084997617455947494821181858444064525533770757194737037597871665'+- params:+    r: '2'+    x: 2/11+  number: '1.050786193652262400764871862066183695695740265705893064553867867085500756023258054733824801839352223'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/11+  number: '1.045081900472368174757478699398120070907417237788141519093612942437713213471904111971556078089367493'+- params:+    r: '4'+    x: 2/11+  number: '1.037973201406283834010388116619437779198833483513001284322157753634176190170913031877999867010352099'+- params:+    r: '6'+    x: 2/11+  number: '1.028061371559877997235467812490300072031750441228370360755887709618727041100989702407199196956397666'+- params:+    r: '2'+    x: 3/11+  number: '1.081154987756952037335394327896449304141077364425785780428448731523391831955526952099289538665511279'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/11+  number: '1.071984369175617240301058194420032415519161751845227138677651698438176623395971863108959965423345757'+- params:+    r: '4'+    x: 3/11+  number: '1.060575365795684179419177558655333970045651873777529084691070779601852013670678030311856368189927927'+- params:+    r: '6'+    x: 3/11+  number: '1.044703686625135244806701095695615524043133715665125128323460448674115255411632110119476910989154386'+- params:+    r: '2'+    x: 4/11+  number: '1.116064294972751678334036987184019823108578304092302884332444163788414765343825632784028634390621069'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 4/11+  number: '1.102862073496377898253471085285026854232749670271011361476607297593240578379269336624743819136117627'+- params:+    r: '4'+    x: 4/11+  number: '1.086467887561676990139742092590604348519321188207866459128776367497925817044791201500433951265299498'+- params:+    r: '6'+    x: 4/11+  number: '1.063717679534189177003166853676704096970216661911781636153997305282625437224110951284829434586684943'+- params:+    r: '2'+    x: 5/11+  number: '1.156972843564388095923427149322346130391954965506711732553570552060545352478125530933061521820453676'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/11+  number: '1.138986857686387145575441200021526791554401695152048963342824066811603058194723902345884560135293771'+- params:+    r: '4'+    x: 5/11+  number: '1.116698026349508783382702147897195456514259307666169063912927046836785925621828003799930846697807366'+- params:+    r: '6'+    x: 5/11+  number: '1.085852694109503816897090320356412402897529051463062715734787375429383093734800408496156128329462475'+- params:+    r: '2'+    x: 6/11+  number: '1.206157630886530125818869972389303717538294388102229398265886485654936308993286211834681097284875567'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 6/11+  number: '1.182342505093989500817360735037737114605461728696797534653525868456243993388825683848959597136090752'+- params:+    r: '4'+    x: 6/11+  number: '1.152897723206490159822570818085382119128377594769358697681085613797160664950378163666265052887406530'+- params:+    r: '6'+    x: 6/11+  number: '1.112274884902382214336712525367454702412361695808694904263080889215295983248233775189017641356201706'+- params:+    r: '2'+    x: 7/11+  number: '1.267460899895319968535438611378616672501836157799738102768656409968900058388790192092353843626673639'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/11+  number: '1.236273815734982676595844207223051262747844837511365292545957883638714865668787720970121533776357960'+- params:+    r: '4'+    x: 7/11+  number: '1.197815801592447954282731837806847275992433052785346468669525631954239479150874876033652459410353286'+- params:+    r: '6'+    x: 7/11+  number: '1.144945761804384534863307731283341063351054694044030220171593350941874301792650369229537129913809569'+- params:+    r: '2'+    x: 8/11+  number: '1.348141232842108551990977939875021899707862668809440574244776569347689319201985389574440550016207674'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 8/11+  number: '1.307094249651611530094248076719487748542299165500513150290411651094082545805765175936547745881581498'+- params:+    r: '4'+    x: 8/11+  number: '1.256635262904252513562281658817613202870375685055264723198871769912858098988377594753529419465141380'+- params:+    r: '6'+    x: 8/11+  number: '1.187558294865867971535413640924808322601117613444200869507885567813962979236242844393906612869894116'+- params:+    r: '2'+    x: 9/11+  number: '1.464631479355372972726029531108621642886383902276560476865346851375978385301147961042338820165628426'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 9/11+  number: '1.409083755732918257279562196466449984646026627172505421412440893913742836941909170984063878340167986'+- params:+    r: '4'+    x: 9/11+  number: '1.341065582053511880591970477711967466551467271249307970289504321908141258488247544857210299353208676'+- params:+    r: '6'+    x: 9/11+  number: '1.248442119965686532979394621641462256011781864276146780741931678886678906595056143104816242135589193'+- params:+    r: '2'+    x: 10/11+  number: '1.669869780325460827882248226975556605010401248986942310359903568133620024908545856235818125462502544'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 10/11+  number: '1.588196520747996037425192428266952001413766176267406643122997986911221632162574780003881023863631072'+- params:+    r: '4'+    x: 10/11+  number: '1.488739273008270502192107813836297641770280602722820880684651859201619882121683149677142023450205425'+- params:+    r: '6'+    x: 10/11+  number: '1.354317975725572261605600824739944885470811372211539934333348402147269535242014756597437334730437889'+- params:+    r: '2'+    x: 1/12+  number: '1.021870277329714933871211801472596079114135093580612745466398921978410563024149678317763851492740071'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 1/12+  number: '1.019428623564650582115552241555020263029813186337083625699923352499207753720690503416460063770942168'+- params:+    r: '4'+    x: 1/12+  number: '1.016380649862763958203394614866063321230008244031320683177072791718776652630354297598681855628065290'+- params:+    r: '6'+    x: 1/12+  number: '1.012121119795324153897807573801663641307652809534553826427844452770469902159869012438396264156873689'+- params:+    r: '2'+    x: 5/12+  number: '1.139077066794801910321708704362096045519657973677261905039448176563141262831351210724591951014013081'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/12+  number: '1.123191332955536330762430668274561754731048153790780541934720918755487015510744462621572554139964393'+- params:+    r: '4'+    x: 5/12+  number: 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'1.017865815072909931233943626040309177904759727252698327763370155671316535572066881017700059335175674'+- params:+    r: '4'+    x: 1/13+  number: '1.015063909112043910329752380504583903059464438272391531486117261888573627410852660958654795516086459'+- params:+    r: '6'+    x: 1/13+  number: '1.011147702553691862694693021558014559154490491290149126085507193567487746464627082515766385347153051'+- params:+    r: '2'+    x: 2/13+  number: '1.042193422634593581173941728438318205007332912682223306261470608447909946955838625252558996635367971'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 2/13+  number: '1.037462634017176756615497488345219493947877967939783041876786930083652363632701013616736121620183857'+- params:+    r: '4'+    x: 2/13+  number: '1.031564186410085935173135737331878099385870517952401637712739394549158245926795950563146900405607148'+- params:+    r: '6'+    x: 2/13+  number: '1.023334374658149254548688827856581756461474427326541225514983127188458413704699316648116270739355181'+- params:+    r: '2'+    x: 3/13+  number: '1.066642645093745941036586777409462423736337611124628262431136681264199707445192615691394090248044245'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 3/13+  number: '1.059133398306179490824202108475302721907471182301008626986835885229666096254617498373568300318841640'+- params:+    r: '4'+    x: 3/13+  number: '1.049783774091424383010647303440092262775864008209776123438693572375754346107864727470306903525945228'+- params:+    r: '6'+    x: 3/13+  number: '1.036763030181206511016844527818669882829844671857922468322467126566513246815626314549239792625168039'+- params:+    r: '2'+    x: 4/13+  number: '1.093977585650621866043767772047057785170375733254121698634665587568703407282034434420244383965152342'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 4/13+  number: '1.083331775453141956548798651000516324767649735588452863624119467166554584390100154171412570148358356'+- params:+    r: '4'+    x: 4/13+  number: '1.070096700220435425892499826589912415135333313560023956808551484460632229700861961361356927209979356'+- params:+    r: '6'+    x: 4/13+  number: '1.051701768750087200685429003950656607320685730122428430809513767095178648450583056503607037247473832'+- params:+    r: '2'+    x: 5/13+  number: '1.124906021881407111376881049044040164593873497193532109851692742489475738877758467797506643802871598'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 5/13+  number: '1.110675120737380195582432667466104838982022893102653969305234230188436289305290197253675535460785031'+- params:+    r: '4'+    x: 5/13+  number: '1.093011568273444772963269437028352254523975067159630530825877405210722395800371867640305278153241301'+- params:+    r: 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complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/13+  number: '1.178686742794826341781312204544414686089031794348372126855172197482924115842973041461090811738117608'+- params:+    r: '4'+    x: 7/13+  number: '1.149848583299468819172943077113498301192583690193135915127451202389680159315719200432568580806346388'+- params:+    r: '6'+    x: 7/13+  number: '1.110052640964092956001916641473138728432129465741305720370197674110271022373261554099407297717057008'+- params:+    r: '2'+    x: 8/13+  number: '1.251941966510046157036632596535264582667013365900994138398781342252469091615815143943269697699483548'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 8/13+  number: '1.222631547105759605999748721490235032170250072241761285772661408306138390468082214314833726061878652'+- params:+    r: '4'+    x: 8/13+  number: 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'6'+    x: 5/14+  number: '1.062266725118523737699974581730114990897962161417790867591020536694941037504428902068676356410316751'+- params:+    r: '2'+    x: 9/14+  number: '1.272461453890228237715142827999164425920664388076998163586392343981316239943484043169653901884645834'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 9/14+  number: '1.240668225164307370000221494546283062153991382258112239008819623990529783304894085084675161849366503'+- params:+    r: '4'+    x: 9/14+  number: '1.201470758852427549563141481694525897783959575591285055972583578785336902192540696151300294420681609'+- params:+    r: '6'+    x: 9/14+  number: '1.147598993250444008603776381429957778606049706091985294763596824419770050403656206463539106619930418'+- params:+    r: '2'+    x: 11/14+  number: '1.417065113963005640602884478638049908496841012485567388317537635621029109310292856766683857881269826'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 11/14+  number: '1.367472401251472832319075900220296509866029992241945587231126002162514111456154510376255760332130404'+- params:+    r: '4'+    x: 11/14+  number: '1.306653785149956055131564905728708845403685071650996315598578949673825932409392644518046942534707520'+- params:+    r: '6'+    x: 11/14+  number: '1.223663619654314575015761602111738900622791238034862748312575329594136212644473439167603710917237755'+- params:+    r: '2'+    x: 13/14+  number: '1.742710866006256297904148690524989786144267935687524599296098590256030695265110854944903932966417713'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 13/14+  number: '1.651631496535268959487989820016879410732581009005858006649553693783820955788854773777888498307678223'+- params:+    r: '4'+    x: 13/14+  number: 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the first kind.+- params:+    r: '3'+    x: 11/15+  number: '1.312683446319700735042845659053906130893211394152161351085675234172233422715662766959645160444124038'+- params:+    r: '4'+    x: 11/15+  number: '1.261270130393394789092098072688134722301926607131945803534418923918290732524928064788967944661622676'+- params:+    r: '6'+    x: 11/15+  number: '1.190908699135308677282035139543141019548803590267457051817698267470191342226225244999885105611778275'+- params:+    r: '2'+    x: 13/15+  number: '1.555625054039474270764282971071874899024793635427561149121165379715885447919195083681140968150244092'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 13/15+  number: '1.488572559350426622331635895820691056107507568596255786926374545395870940432300191430535294280697481'+- params:+    r: '4'+    x: 13/15+  number: '1.406683465745524759773908950699474888448585876066299675963867643112659006428329431299186908498125026'+- params:+    r: '6'+    x: 13/15+  number: '1.295570522690796564480299205190722046620505780257701036154485158100074624466470571682388039926908571'+- params:+    r: '2'+    x: 14/15+  number: '1.763662272425612825015627157523997331881953816798130553323621032498697905788660652699087137076933613'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 14/15+  number: '1.669866980944424833657833255953531498140640822417128094475176023161235212388373555445744969418474361'+- params:+    r: '4'+    x: 14/15+  number: '1.555884066878087146814368912089640920790274333520447842513291995045858721979547517984163728435474162'+- params:+    r: '6'+    x: 14/15+  number: '1.402264341872106165712890646739097836281878847044122003941951024171928753773175776048263103363617459'+- params:+    r: '2'+    x: 1/16+  number: '1.016199360097058232069473923609701162536348851915089087262799285576704585360569233724687760164709106'+  comment: $2K(x)/\pi$, 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is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 7/20+  number: '1.097933076595116867677920653218324945692050500336941282626965624999874935524165165027229424829801917'+- params:+    r: '4'+    x: 7/20+  number: '1.082338073263144500473831205653758182994484664857657347970658251212062998024714449287864234369772724'+- params:+    r: '6'+    x: 7/20+  number: '1.060688490091388067704201217291994405405828519017305873235576430858182552955313616856025058470060144'+- params:+    r: '2'+    x: 9/20+  number: '1.154754378957639790044855173713824551480466482988060233564316471798294060325679291469065439429278075'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 9/20+  number: '1.137029373243031782287418947980166112696049897629836352725663496123549230406037829455265658119365125'+- params:+    r: '4'+    x: 9/20+  number: '1.115061589732827065338196878851480002604492268282666173172449649996900854691439409384538362193516897'+- params:+    r: '6'+    x: 9/20+  number: '1.084656154971247807414290135775368167630791189418175886523758962561412160244925754539302277722881481'+- params:+    r: '2'+    x: 11/20+  number: '1.208893144120206232516306408908837768180273166082994846268712718083353972297833321527288318451408631'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 11/20+  number: '1.184751491399005991938464830189911325712169473094346201589788757023955694906881486384213102500834906'+- params:+    r: '4'+    x: 11/20+  number: '1.154906658383825711045063188161117689285321064289920495839402404092224265518907439979368147638866764'+- params:+    r: '6'+    x: 11/20+  number: '1.113738694252525242041295670796081209991090141681116551352411912781649906834096786714394649792298522'+- params:+    r: '2'+    x: 13/20+  number: '1.278076835410447316078793692074485929087733337978697251151369571802296811486588625027312326239558693'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 13/20+  number: '1.245602113862525144571721701417204989232621070999139319312608443305409659507776692298529286527362059'+- params:+    r: '4'+    x: 13/20+  number: '1.205573555615801618729952409315006020104354192691429579253692537420185342695144626030347645398717037'+- params:+    r: '6'+    x: 13/20+  number: '1.150576439011235964792882965551513607590184353282936060439318541754878196867199879049683818289979105'+- params:+    r: '2'+    x: 17/20+  number: '1.520895131706989785265585357180785292577555282365086745968252303894393407419229800951214530403499361'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 17/20+  number: '1.458249973741845631469921584885728930382222493743938446775256764021776926260972470350864553272565088'+- params:+    r: '4'+    x: 17/20+  number: '1.381669185212568089882110244428396789654846495655559904120696727254088215907445318453684477568887479'+- params:+    r: '6'+    x: 17/20+  number: '1.277621963605922934342149087711348852167024528004346008823060001311214976458555818641812891390662048'+- params:+    r: '2'+    x: 19/20+  number: '1.851504997072928624504447168973920255102443321185458361659457162426346798503144595800969965361656560'+  comment: $2K(x)/\pi$, where $K$ is the complete elliptic integral of the first kind.+- params:+    r: '3'+    x: 19/20+  number: '1.746278186220003675115938355491152316755529013253150593740976874905771172753221706299820981826218055'+- params:+    r: '4'+    x: 19/20+  number: '1.618623452857967343673983386289841485251115958985900657894359182074004821192982460565693227071687752'+- params:+    r: '6'+    x: 19/20+  number: '1.446982117982091449688403200842536797386601725787857737480753842321516489423287027526302127497989144'