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Values of modified Bessel functions of the first kind $I_\nu(x)$
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Numbers
$\nu$
$x$ 
value
0
1/4:
1.015686141223607923354734491287226289488594947237910002922426945499074607205960302420009002658735535
0
1/3:
1.027971275421311545458243227919407439316929694410135122751513086229082717055169924252453398303877964
0
1/2:
1.063483370741323519263184415445356529329523174821104989169572074687926718505691854434563831841333863
0
2/3:
1.114235900602199292353846835940049312704478667256703770698919588572472407059638026338247427389805875
0
3/4:
1.145646778044001327647570800381518388496279781934335455507070358273356206772348296280891149546386190
0
1:
1.266065877752008335598244625214717537607670311354962206808135331213575016122775470394818357147280102
0
5/4:
1.430468717721829681772097928201953563980792068528956610750170148450999517181357861264044412097487726
0
4/3:
1.496334772765747320523716285638270889514445798511491675577924175762382635472885016746055965914661536
0
3/2:
1.646723189772890844876306125493315463109825314339320039961375306479816923596184888844748735104496189
0
5/3:
1.824725636697877426451179821477681237286441326470983810188249799891171511990861738467853996778185631
0
7/4:
1.925252153858502413833985871336446758426219219605378809421965106159460601606537394854211277531087114
0
2:
2.279585302336067267437204440811533353285841102785459054070839751664305343232676342729517088556485899
0
9/4:
2.727078307190795428594650835049732002051028429442013939913992159221893967308999099534530577638769944
0
7/3:
2.900607888842885682481036149148810758612130060594533507575842624852196299213644456636694096434406450
0
5/2:
3.289839144050123035705908229906056026111801575348394161255287053440538128106949733240705134178381222
0
8/3:
3.742612878920084581061869005667314990057232241561800292758766634798346414503676442179922750050973656
0
11/4:
3.995913107237656049697848908925237694811641581155558224237335686340255506757290286853901189098191229
0
3:
4.880792585865024085611235546021319249424328856405997616059563816165892577968582703734289632694045590
0
13/4:
5.989335997939518439773984968492402535525368001083221384430874080620766759168549080080287404001039647
0
10/3:
6.417951388809747209950609519137013345577548194950258933997589389683755225699614264709229876240688604
0
7/2:
7.378203432225479660343837846163019914144675516730028685246917870521090119231785633065824192362068633
0
11/3:
8.494459907937252943553485725681332466385977853528089231427105960893154022356072587938381167228675026
0
15/4:
9.118945860844566690670997606600087426155299165593330527335934943006484827889670821314221499449952375
0
4:
11.30192195213633049635627018321710249741261659443533770600649619347053446508218367074914826930622669
0
17/4:
14.04126368300061137126651651061295832342290195705278012414896713457106937348657424783240616549918987
0
13/3:
15.10192889272115624311584590480647392836001676902654228439754123665107709568925275747378604714396724
0
9/2:
17.48117185560927604313311908699420272654437797274949237136821839606268052166425259762622579059937080
0
14/3:
20.25179400203644928127246130290139803930772870734652776290860864933495281694201994887654836573851999
0
19/4:
21.80389874090211391163620951100917996495624191440606105427963439343584578395370840801163725312814674
0
5:
27.23987182360444689454423207588441928247906183222098381517165811040289984070662927197843649715623557
1/3
1/4:
0.5665068655780870758444762867295816712724976306962208288449736832137884166922678375913445467907571150
1/3
1/3:
0.6291909949874264358705844453842230200154781624186961576784161507937421150720577585367833352117637291
1/3
1/2:
0.7389731564251193223360002054570566340615634380483598963693352865416512542526547592342132347541141861
1/3
2/3:
0.8427208818885967060697065235482895229643701888385384782821230460793215845423300189078998323292777562
1/3
3/4:
0.8953232036583689452202881657516434231803054035119980583015747337926464429092637689028575260069144043
1/3
1:
1.064631397889529513822473798351438566976664238677892667322233195975278978495654815322385566032285148
1/3
5/4:
1.262377673260525984318348793402869119474213459353072699406472044316963041449268613606898571700089243
1/3
4/3:
1.336840714590219130179414809012954542264780011005200529575444893526271220096473083613845185502749206
1/3
3/2:
1.501429000022440020688070478245074125516329490619445560919347616820526099718177714565119094338596903
1/3
5/3:
1.690259555783208138416613210414965956048036037289252318342400684314841610171906842274567201928718188
1/3
7/4:
1.795119552594605335423729383933281805500463328940049025821073210300379664899278542566245075556832668
1/3
2:
2.158782581372863023950198016899693641972738082091303243020112931781890315307981293961322382100307146
1/3
9/4:
2.610913456481142958413565066784814615060905252932124075435729058920085352440938164794435648247480959
1/3
7/3:
2.785077788768440249204725101642353400245176275422004536832351975262072169659057150994505387904523520
1/3
5/2:
3.174324229724197135699310785048456785074495545814161006299297855407614083186389008055944051545638850
1/3
8/3:
3.625521076996505451370883907544081768408783370336270417782074467394309966475115640052436119274765048
1/3
11/4:
3.877455172218214832195831076271381324534460549298121976630411886301590082905559509898554122956232012
1/3
3:
4.755956937164698623044132523295031232489669740770556924310299381778672849594760341884717821828059440
1/3
13/4:
5.854649965273189428520917565499313293999446360200518232102368884116576718153474446417199512530048291
1/3
10/3:
6.279178043425752636794413988645972517911923007687378911479213264717393700465947195336252832916047291
1/3
7/2:
7.229979861917122453018479232312879665530152385811393824849970524035613850823564621227445013083651572
1/3
11/3:
8.334979402829903179569758498469884590618480626164191032355270427501677135076054445860304155109023453
1/3
15/4:
8.953111435550633725377381903696257009746446445859724108482430944065873969325692720369912237921322469
1/3
4:
11.11383838999148187872594270920849188387304434766484071915772721590059745308959994029619124569921019
1/3
17/4:
13.82553113652911948179397763959745246691185533498254157916691459955817247821447239778299018242971423
1/3
13/3:
14.87561672062938644642100223514743438294683728056289421028799479953361015905125982889097860112814143
1/3
9/2:
17.23140396847831783725032320075354618190923143713999067434894777511932168312333766786287111676298725
1/3
14/3:
19.97518247801435081649701233907435282663941266154151500048976529948008270343342320552996728791736993
1/3
19/4:
21.51245809955654849040684720048672890080396822165415668130447072836489138972610339655355717286105592
1/3
5:
26.89755306926836466115586016833602046773128329610247435904758729001311243327134133908481319937198590
1/2
1/4:
0.4031109348997593047996807317994119625080558590068025919966614742837005573353729363986763893049032979
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
1/3:
0.4692371041609475144373497046949520478987256490625579189702305832053072871747952069572883021763031682
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
1/2:
0.5879930867904163254888734401632344980939760733925167921392208938692037832750531278426002540515668051
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
2/3:
0.7008108509648546794388742185918791293290743907054080775033428081130781056136698386014857683386589676
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
3/4:
0.7576149863899140073245390114216699661006219652315390889863460384861977671501205309609190923477044753
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
1:
0.9376748882454876467172628843913933678317891528316871151473032695467443653752368457326147699504648436
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
5/4:
1.143208985315988207436926523703278965543026198338701396470915438825794840700287637772268171487937263
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
4/3:
1.219618793613905224248463121828990835076815158078300942886562325584520077224718456341442623165591535
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
3/2:
1.387161720403477880892971563987771268071906873761715793988104842772590248050631901215397285813304059
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
5/3:
1.577733717277839392192349752743560727078499294037544392571702601342084228719574970202762313020928787
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
7/4:
1.683021780455683263283492965261962021384607781093098520631331952241169571233992804683881214551361122
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
2:
2.046236863089055036605183612020732319267539021494681248971274579779499822359710790528214575225608185
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
9/4:
2.495340508936007666823704160640973833377746379847649799726062470142143020269134064379452104836061798
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
7/3:
2.667916457396821760169277512074649538274709219883093464219310999514466817127140829181590348341610619
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
5/2:
3.053093538196718436191492425872240564119781482739840267961952176862107926171149042439144947113119042
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
8/3:
3.498988283191578048388178794589514993682961204688352007408653245607547402309915380947733656572760128
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
11/4:
3.747788249487948165791913175733067516750402066320668757982138574578336773541637911236435113945625705
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
3:
4.614822903407600947852980300249277034594777812261613271704516793644147332457608995123428639456357452
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
13/4:
5.698650532533554898753877430297935085880405225712511379313536758422280440136082666989848170483902485
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
10/3:
6.117386444003177790947154319642020308426846934515769332077577400380959057969315465142310101403399410
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
7/2:
7.055219408691195823286009098298519699245751825381950624120197214344092120393450930077126831944102899
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
11/3:
8.145234528954201755925005612814164305969721315197418370515980550192935634813876583201236182260794380
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
15/4:
8.755046784118905296053962120825300171437445379771333909191900895388435976186990815185630759706122434
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
4:
10.88710179858841955444542990122482704154505736872626019859714242262091238938105551230591493914027430
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
17/4:
13.56371871257976098634877657379095058610243687341028434173093239783931231971415215658552198423800289
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
13/3:
14.60047436065498201095540257508653660364206097899018030033593403578782730878775386978628438818900104
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
9/2:
16.92682008015818495966147873654906834455681293868763924391117481114511494104492808320467349769086708
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
14/3:
19.63703221102501059947660932518994743476207221257819055863681934608920275743768739221418002570977629
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
19/4:
21.15580430657000077856903324683586232437952833979683002149709890299378431326587545390497635351556895
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
1/2
5:
26.47754749755906520538649923039889193236403851631847316637275461900744171260619503061560644632060291
comment: $I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$.
2/3
1/4:
0.2795369061320046271864200932288622742962814429281050905883550672375059792927427422322654766087119696
2/3
1/3:
0.3411010254963778139895936234766412157152849057951943565569609101680523340905083314712128209641518368
2/3
1/2:
0.4562832311355691809763239033987047553013460318294986548523323928031748516806665444565699413112160218
2/3
2/3:
0.5687920437744086374255366803567034557036662976712184237654582719170068770667422662239440572466681619
2/3
3/4:
0.6259456983818266271701949547726050927026168302293888410549145382752674904847019297694437608220513061
2/3
1:
0.8075212886061302620691930614360108001411150233582232025146261126229352335713186150735728618626544468
2/3
5/4:
1.013948451357718134807428316741371775839756021423404379225626366338433271906579637832977400691511387
2/3
4/3:
1.090349729974359177156006466016244601915244429156463097103233405174351532598202376937983902941693565
2/3
3/2:
1.257291839696300606960142327248846759007639055375047737905702111757672098965615380278604250376386991
2/3
5/3:
1.446388393991262529684633306835995404033965284542976600756213445447102172586791888275063698170793565
2/3
7/4:
1.550580693832559834379574844961173718600990838322514757730758076751713795871941137692845906255160948
2/3
2:
1.908949296823621974645372546971666318184749070883734348808494383478272348614467021303159039180179682
2/3
9/4:
2.350646349030035452438230277295852593400161083459173528678280663777214730940022304208196129149030428
2/3
7/3:
2.520131513117596511814322740932256117568036833058882305253373739382154828551371728002697385554806559
2/3
5/2:
2.898116189422492328996916841682379485316527290122677367369608102168763350676085465508840522193313592
2/3
8/3:
3.335370677001383205740860863336864334959113810605145609002564713720596099900277580459972422124344893
2/3
11/4:
3.579265491106875409639656119579139607073368705495882940204451284910527948888025848426810867630634715
2/3
3:
4.429008721354955282938554602590528173272825530474015959233192745322830067557558590135950043911675822
2/3
13/4:
5.491189572009773136643130303905904688263903551295109475794925699018724371795352044306741621281087529
2/3
10/3:
5.901614996034897284749286712742492609379598643032437696523454340776593679959556664396691233150092752
2/3
7/2:
6.820991804413739935002346821011179341157126390155034129361585562822841933779787065078552446182170421
2/3
11/3:
7.889855904633059214137161312676228594743523419463014683596923356291767286944912416097006424656795175
2/3
15/4:
8.487978424961983403233352598129142422363755667234934263343600297727939574929696970431542861577523921
2/3
4:
10.57993277401301569205009814578209955937044514701899290296251288202869218905852702331258117602042258
2/3
17/4:
13.20772035548245779420665014175772768469727481262011258248640959273898536832006887586273396899426165
2/3
13/3:
14.22595750216154218697867978534207694994820732245843059490938059161702256131169295355217187753781252
2/3
9/2:
16.51144840420054830371150398114937712589799705346724009749204419868750965860452221250502497093100081
2/3
14/3:
19.17513430713714665481550780701898124799626811757524825871811807879842494840577646288030475369690348
2/3
19/4:
20.66827453283238989089280529506549149737044345255292999108370598344993237735663734258833382960855854
2/3
5:
25.90231058321512939718296370436207357282262118685251309452065017841769312212342585473297372207556488
1
1/4:
0.1259791089454679259077071756314495044065532094148493424107896798052363469360698042494143755957617080
1
1/3:
0.1689922230584792334496878171890807032094366545928099519383810669331196525423707817445071055600082674
1
1/2:
0.2578943053908963163624796595232096341877431496407945727309451908705658633894396867253622830158284815
1
2/3:
0.3521979804151622898722155940638156162152875363442325821567222313164151087300673773991143744425136070
1
3/4:
0.4019924615809222052521049056996070505153984698592972704812894555246799471561429689756960128064133061
1
1:
0.5651591039924850272076960276098633073288996216210920094802944894792556409643711340926649977668144101
1
5/4:
0.7552814183407471915642979174086482503431007413933932962958556489825906393173593484830090271170045679
1
4/3:
0.8262043611042785562881350222464638561229955707101717879155102994790438567401054438702920915633670257
1
3/2:
0.9816664285779075856520109078674034841349457649523762049019689585192554738131336253237863479925027181
1
5/3:
1.158181927650729547911189659195997812574288356928339031428609207533931083747174392206754061888443897
1
7/4:
1.255537512240172999863214333779046464728727165103863659273601569695839866558473399424449410246667948
1
2:
1.590636854637329063382254424999666247954478159495536647132287984608545037535361185116122147594228925
1
9/4:
2.003967456929593057596656694498419627909505550625440728207702251705892661209985488714486789666863666
1
7/3:
2.162649701472147064335247011796091944136107751556257804922499997928697880087141151651476711738834922
1
5/2:
2.516716245288698441528191748122377672388947303396949218994539553686212362199848980547861132862365488
1
8/3:
2.926619513078510671644853001467918373662771328813767462251321051955008551233821768889399220852863536
1
11/4:
3.155410138619003261033505333105722335391644777522062024660644199080024604121697596448445666301752562
1
3:
3.953370217402609396478635740580581287584221595091259177585845489515361796831023843583030512645192202
1
13/4:
4.952546165908548023620690229516611860078157883491335523571940214354534105393480036434282380200432973
1
10/3:
5.339094217109160954816577276144049812602089145409213610953890139624036429472353271545932725717277103
1
7/2:
6.205834922258365473622609252648831983497743921809655530460535303685186655875686077723197459546693745
1
11/3:
7.214834374134345368704586385010720696841087554900705515821452723742938737987933356470359948026391238
1
15/4:
7.780015229824415864988676277516113103258589291140045631174696530407796076204896802551568774786996577
1
4:
9.759465153704449909475192567312680900055970333252967306927528051449699946606323486237095555864214553
1
17/4:
12.25087466740930823804556035590270396804923127484417507748001680948175638787537750705240316214424355
1
13/3:
13.21749233973029257671642031945891753597610450616399546683012778834908589228525442598663531585991792
1
9/2:
15.38922275373592389269384693779984264150591710918290449978443444577322709392313425107428151282193886
1
14/3:
17.92348573395164784464711905501004878934288563263217582050465631966208300865323875432876795142704280
1
19/4:
19.34536144752022556178088901044594601650969651942303401438972939998074610867736461103326283646487932
1
5:
24.33564214245052719914305045176000846056487436829889815840308023040396296871684167861720041842474864
3/2
1/4:
0.03345343680843306508459336951700089069481363730018225856798023511685358217562350312613295451133786038
3/2
1/3:
0.05175529454319556096127175187594137883730008779378796107979441393980189333890328283809623152009330535
3/2
1/2:
0.09640347383401674086962892677695961777749362123102707647233861636347311926688751324663038263383953802
3/2
2/3:
0.1513083625441424603330579634931233082926023987657458033376390929973108009311560116251307981708418207
3/2
3/4:
0.1826613522112649553296903232716560925050337718887028068950704870961365651605707749256389986309495931
3/2
1:
0.2935253263474797997886288580631092360156155582660783061556621551522615651749063585154647966760398190
3/2
5/4:
0.4331058440518839996758568725742530480361193843346619091599050814299975534612829284820185334721320551
3/2
4/3:
0.4870472364762186408055107004405806361347872585768916306202332892239060095228026130741155536507449163
3/2
3/2:
0.6077498491075907787361625129286393744504373127939169711916897610726663511603702848650404583584146171
3/2
5/3:
0.7478259233395006860668375295823590412159435877850269783455566190687095633396301890329984942974050965
3/2
7/4:
0.8261057662132905690048015069468746371637628631345925858870213503368055432052085366781300295714594054
3/2
2:
1.099473188633109675513528489721211781485356148906477764373097084954793493661969907005873948043187911
3/2
9/4:
1.442364558741230284949588092829157537852956990325442621324401285007012661592057646726635858814202809
3/2
7/3:
1.575175839173303282419509204451669789512209670050733968176089924113206620674052130507920974545998576
3/2
5/2:
1.873278388837618888527191316287481580391257299492427794004552449184239050645411724308247792223386167
3/2
8/3:
2.220817465797881122919941730887572729695011748554880403751305607184485824833353277585922781023354225
3/2
11/4:
2.415714569309601093731499166322231514321687880811076672932976640236210385072949944443996252327659502
3/2
3:
3.099483456725635810112401647595276667152046094095838219043503230462450061347586037253396254315040694
3/2
13/4:
3.962380549005850688908101616606652944268157685190976679346428990834874168201499771743720969780151666
3/2
10/3:
4.297760736980021604319038882669496663677843384388011202919033025285319290566044233106728778600388655
3/2
7/2:
5.052321233407263720381166278805502616816709913565052864706962095328631253902454181982621044320824384
3/2
11/3:
5.934457951271004275191105760517343490194177399597302892788214496765536281954725942469246936855644539
3/2
15/4:
6.430057560102038915074928083330578099453549524871015637825511730010294025373593361017378166502550775
3/2
4:
8.172633231686595442001664942747810150032565909203784580359621642149661596094685894288610039456937044
3/2
17/4:
10.37777618482630857015461944209030244135080843477651139658819274463759577189257427269744760708741636
3/2
13/3:
11.23616433521992111348280379197635986549283464965824747332246129185425388431910571621851221002967223
3/2
9/2:
13.16948289354339567517038825742355848612475862628775855877693399189924066008315146574079126981456696
3/2
14/3:
15.43256993160733250377895703770041441776679460121143473810196570068041487375370178104552644201185952
3/2
19/4:
16.70511810675599913584568059202161547722329322076783720814933892762974332420020753899557627839316742
3/2
5:
21.18444226479413767940219691374088938372785389790493935672583190868093060030063645008011919927411378
2
1/4:
0.007853269659864516093077086235630254236169271919115263636109507057183831717401868424693997892641871103
2
1/3:
0.01401793707043614476011632478492322006030976685327541112122668463036480180094523378541076494382835965
2
1/2:
0.03190614917773825381326577735251799257855057625792669824579131120566326494793310753311469977801993717
2
2/3:
0.05764195935671242273720005374860246405861605822400602422875289462322708086943589414090430406226505400
2
3/4:
0.07366688049487544697529105184923292045521719564287606755696514354087634768930037901236844872928404089
2
1:
0.1357476697670382811828525699949909229498710681127781878475463522550637341940332022094883616136512817
2
5/4:
0.2220184483766341752692212603481163634318308822995273366768011100788544942735829036912299687102804172
2
4/3:
0.2570282311093294860915137522685751053299524424462339937046587265438168503627268509406178285696109979
2
3/2:
0.3378346183356807306736249150034441509298976277361517667587500284541429585120067217463669377811592319
2
5/3:
0.4349073235170019689577522304424838621972952981569769724739187508504542114942524678197491225120529545
2
7/4:
0.4903521398697332711331694898746793701648167452009631988235633122213578969682820812262690943920380309
2
2:
0.6889484476987382040549500158118671053313629432899224069385517670557603056973151576133949409622569737
2
9/4:
0.9457739010311571551754004399400256661314679399971777370627012688166560462334564428994312090460022410
2
7/3:
1.046908144723902484479395853323589092209751987832026817642271198056169544853237755221142629229690803
2
5/2:
1.276466147819164282483354831408153888200643732630834786059655410491568238347070548802416227888488832
2
8/3:
1.547648244111201577328229254566376209810153744951474696070275845832090001078310115512873334411326004
2
11/4:
1.701069370060199132582572303030166905435899924775876751756867177918419431032419307618667977242371184
2
3:
2.245212440929951154625478385634265057701514459678491497669000156488984713414566808012269290930584122
2
13/4:
2.941615280457335040622790981097564467784963149703937985309680102556438078926407519197652093108465509
2
10/3:
3.214494858544250637060663153450583458016294707704730767425255305909333368016202301781670240810322342
2
7/2:
3.832012048077842246845203987506544495003107561410225524983754839843840601588536445795425644049672207
2
11/3:
4.559095703863973651532802242948212086290839187218613495524495384306096528908108938954548468305188897
2
15/4:
4.969604404938211562677036925258160437750718210318639524042763460122326920580392526620051486230220868
2
4:
6.422189375284105541618673899560762047384631427808854052542732167745684491779021927630600491374119418
2
17/4:
8.276146192455054553362723401952862338458557827714344793570135694814948720368749538631275265666604673
2
13/3:
9.001547812845636592323651911210050450217199304643159761245174565105345145403750714710723593670158971
2
9/2:
10.64151729839330986860252044797205044143063703533486814924180308683013514658730404159321178490073131
2
14/3:
12.57030011605717163356655313646851998673220629336130955412089879805120295609063191130707638655550165
2
19/4:
13.65848339457780841193899308555825532642584337991215199558922201449658426451060751915552658514293440
2
5:
17.50561496662423601488701189518041589825311208490142455181042601824131465321989260053155632978633611
5/2
1/4:
0.001669693198562523784560297595401274170292211404615489180898652881457571227890898885080935168848973393
5/2
1/3:
0.003439453272187465785903937811479638363024858918466269252080857747090247124665661414422218495463420085
5/2
1/2:
0.009572243786315880271099879501476791429014346006354333305189195688365067673728048362817958248529576964
5/2
2/3:
0.01992321951621360794011338287282424201236359625955196248396688962517950142346778628839717656987077435
5/2
3/4:
0.02696957754485418600577771833504559608048687767672786140606409010165150650783743125836309782390610302
5/2
1:
0.05709890920304824735137631020206565978494247803345219668031680408995966985051777018622037992234538653
5/2
5/4:
0.1037549595914666082148700295250716502563396759355128144871432433938007123932086094154236911548203310
5/2
4/3:
0.1237625115424132824360640458376844037735438262802947739910374248307315557984125769246826274514154736
5/2
3/2:
0.1716620221882963234206465381304925191710322481738818516047253206272575457298913314853163690964748252
5/2
5/3:
0.2316470552667381572720421994953144528898008360244958315497006870184070147082406299433650232855996135
5/2
7/4:
0.2668404669471851449895475247816055005324428728623683733964382088066457828822067418070868781431449989
5/2
2:
0.3970270801393905233348908774389146470395047981349646024116289523473095818667559300194036531608263188
5/2
9/4:
0.5721877639477006202242533702020971162404703927470596379601940901327928048130572020772709597504580519
5/2
7/3:
0.6426903784597175399156228206367883803304396441035783622786239542260583048319309470999776667824695930
5/2
5/2:
0.8051594715915757699588628463272626676502727233489269151564892378410210653966549732692475964450556416
5/2
8/3:
1.000568634168961785103244347340995672776072987564111553188434437525000849372392943663570527921486625
5/2
11/4:
1.112463264786565154448459539745178592035833469072221478418891330684289080734783426388439202315451703
5/2
3:
1.515339446681965137740578652654000367442731718165775052661013563181697271110022957870032385141316758
5/2
13/4:
2.041068487297385032069475938045640060402105823997763675301448459190088900257775185380259582994531717
5/2
10/3:
2.249401780721158347060019325239473311116787888566559249450447677624171696459875655346254200663049621
5/2
7/2:
2.724658351484969777245009430750946027688571899469048168657086846919551045619918774092023079669110569
5/2
11/3:
3.289768932459743712586828172390883268538121624617806912780168689202951404123646266635488688469812485
5/2
15/4:
3.611000736037274163994019654160837691874605759874521398931491511380200755888116126371728226504081814
5/2
4:
4.757626874823472972944181194163969429020632936823421763327426191008666192310041091589457409547571516
5/2
17/4:
6.238229640937660819180809908786031215737160331215099826492208107506891774848805611152029555705708991
5/2
13/3:
6.821591359348882778544230719102902850608560067688316664958845449119497696566834527788852858168458731
5/2
9/2:
8.147164817795921176214553231600029353806973854495800204726552149878954500989493772710812651147822445
5/2
14/3:
9.716094397848868275618708372382538166197704254656553941285555681366078910024593390113484455845009450
5/2
19/4:
10.60520339703989606119281392555905254929113262141714336371856905396447274008679700822355975663567374
5/2
5:
13.76688213868258259774518108215435830212732617757550955233725547379888335242581316056753492675613464
3
1/4:
0.0003267943876356684184737958613654366278448587090051242330375668902950394576399094543104093134917703226
3
1/3:
0.0007769782132454963282919197700020624857194523535050184836608513687420309310279763195779262340679515720
3
1/2:
0.002645111968990285856353440703065693559338539577380986764614701225259743805974826460444684791668984137
3
2/3:
0.006346224274887753449015271572200831863591187000196436784204863577052623513452012553688550068923282998
3
3/4:
0.009102432274919821383885962503698141420906759763958243510808689973339426146540947576397619583565087973
3
1:
0.02216842492433190247628574762989961552941534916997925809010908045900070418823832525471155131220928310
3
5/4:
0.04482238353551783070278988429467588736124191803490581893009209673025625764189405667107312724410723286
3
4/3:
0.05511966777629009801359376544073854013313824337146980680153411984759330565192489104843860585453403200
3
3/2:
0.08077411301609230385567780119155241498855209098930482687863554930820758444778236733347451390941143301
3
5/3:
0.1144043512099248224125843061340365433007796413515942974912042054928409761609684694393561678595168063
3
7/4:
0.1347326211093540944159697854940650472091460332159477762483139989041646734881143566215486230648667343
3
2:
0.2127399592398526552723543933759320372917522729156918332551844504970244261407308698893322656697149777
3
9/4:
0.3225916328742025595070559123828184436757847684082358623184555515873930234616184791154979735850819039
3
7/3:
0.3679500248025999480848541203842249289193900581299261175357493726895500889101621427009464902022221174
3
5/2:
0.4743704087780355895548240178693314512679173311876135612990908968997031808445361024639951682407833571
3
8/3:
0.6051471469117083056525091196183540589475407113865554181459072832068735496163565956200892192358745301
3
11/4:
0.6811274185314408863679456196072977456666994323935140221052010311986872498927240580940195175855762945
3
3:
0.9597536294960078569779978930682278773155356488532705140271786141967155122782680995666714580710800386
3
13/4:
1.332096589961058742854178252781147899727434006932642618575410857361994931330209243575633650220783115
3
10/3:
1.481700386856060190343781492003349662982535496163536690043583772532836387852910509407928436744890293
3
7/2:
1.826392581597974334370947552641352560637049565912254930479101201006511682631644425385568152061354080
3
11/3:
2.241275424464555930668802119976307511796535714298581702522003213590833433724541786701761618966185168
3
15/4:
2.479103864556990198133170223907408636324489866800163472195748839610647360919144774156847189474760985
3
4:
3.337275778420344367856518667751918852671338905444113254384795883704015454827301558606495064490095135
3
17/4:
4.461560603922198070174761859947068825970588613465968212943418508479451709881260294222967617987439155
3
13/3:
4.908371281718935722263818555265024812698689763416463379526889728251844219604869150869044306318232714
3
9/2:
5.930096266275204009491606539602464471345350855551910589347276146368662519178863991880315481799066578
3
14/3:
7.148942777331215015875787795179888800715280238322481916972457349903909046289839973208416762950898525
3
19/4:
7.843480694191544793832263254186362583730038936339116544419858229878359359615800384375977291081355622
3
5:
10.33115016915113838723344093561567574196238470037775851695473941581091124614092759819195535459567975
Definition
This table gives the real principal values of the modified Bessel function of the first kind $I_\nu(x)$ [1] [2], for rational order $\nu\geq0$ and rational argument $x>0$.
Parameters
$\nu$
—   order ($\nu\in\mathbb{Q}$, $\nu\geq0$)
$x$
—   argument ($x>0$)
Formulas
(1)
$I_{\nu-1}(x)-I_{\nu+1}(x)=2\nu I_\nu(x)/x$ [4].
(2)
For an integer $n$, $I_{-n}(x)=I_n(x)$ [3].
(3)
$I_{1/2}(x)=\sqrt{2/(\pi x)}\sinh x$ [5].
Comments
(4)
The principal branch is that of [2]. For real $\nu$ and $x>0$, $I_\nu(x)$ is real. At the origin, $I_0(0)=1$ and $I_\nu(0)=0$ for $\nu>0$; the table begins above $x=0$ so that it uses the same argument range as the table of $J_\nu$ and the table of $Y_\nu$.
(5)
Negative integer orders are not listed separately; they reduce to positive integer orders by (2). For nonintegral negative orders, the connection formulas in [3] express the values through $I_\nu(x)$ and $K_\nu(x)$.
(6)
These are the ordinary cylindrical modified Bessel functions. The modified spherical Bessel function of the first kind is $\mathrm{i}_n(x)=\sqrt{\pi/(2x)}I_{n+1/2}(x)$ [6].
(7)
Half-integer orders are elementary. The Bessel polynomials occur in explicit formulas for the associated spherical and modified spherical functions [7].
(8)
The von Mises distribution on a circle has density $\exp(\kappa\cos(\theta-\mu))/(2\pi I_0(\kappa))$ [9].
Programs
(P1)
Sage
import numberdb.sage as numberdb
from sage.rings.complex_arb import ComplexBallField
from sage.rings.rational_field import QQ

CBF = ComplexBallField(numberdb.bits(100, losing=64))
nu = CBF(QQ(0))
x = CBF(QQ(1))
# Sage's arb method is called on the argument and takes the order.
x.bessel_I(nu).real()
(P2)
Python
import mpmath

mpmath.mp.dps = 100
mpmath.besseli(0, 1)
Links
Similar tables
Values of Bessel functions of the first kind $J_\nu(x)$ —   stores the ordinary Bessel function $J_\nu$ over the same orders and arguments
Values of Bessel functions of the second kind $Y_\nu(x)$ —   stores the ordinary Bessel function $Y_\nu$ over the same orders and arguments
Zeros of Bessel functions of the first kind $J_\alpha$ —   stores zeros of the ordinary Bessel function $J_\alpha$ for real order $\alpha$
Zeros of Bessel functions of the second kind $Y_\alpha$ —   stores zeros of the ordinary Bessel function $Y_\alpha$ for real order $\alpha$
Local extrema of Bessel functions of the first kind $J_\alpha$ —   stores extrema of the ordinary Bessel function $J_\alpha$ for real order $\alpha$
Local extrema of Bessel functions of the second kind $Y_\alpha$ —   stores extrema of the ordinary Bessel function $Y_\alpha$ for real order $\alpha$
Bessel polynomials $y_n$ —   occur in explicit formulas for half-integer spherical and modified spherical Bessel functions
Data properties
Entries are of type: real number
How well the digits are known: proven
Table is complete: no (it holds $I_\nu(x)$ for $\nu\in\{0,1/3,1/2,2/3,1,3/2,2,5/2,3\}$ and for every positive rational $x=a/b$ in lowest terms with $b\leq4$ and $x\leq5$)
How they were obtained:

Each value was computed as a Sage real ball with arb at numberdb.bits(digits, losing=64) bits.

more

The entries were checked against mpmath at 150 decimal digits, against the recurrence in (1) wherever all three orders are stored, against the negative integer order formula in (2) for $n=0,1,2,3$, against the elementary half-order formula in (3), and against the OEIS value for $I_0(1)$ [8]. The widest returned ball had radius less than $10^{-115}$ for 100 requested digits.



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