History of Values of the error function $\operatorname{erf}(x)$

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2026-09-11 09:18 bmatschke (no message) current reviewed
2026-09-11 09:00 bmatschke with assisted by an agent republished on the grid the generator now describes
2026-09-11 09:00 bmatschke with assisted by an agent removing the arguments the new grid drops
2026-09-11 08:54 bmatschke with assisted by an agent republished on a new grid, removing the old one
2026-09-10 20:23 bmatschke with assisted by an agent values of erf(x) at rational arguments
2026-09-10 20:22 bmatschke a finer grid, at the scale this corpus holds
2026-09-10 18:51 bmatschke say the Fresnel definition here rather than cite one that moved to another table
2026-09-10 18:48 bmatschke restore the entries an upsert dropped
2026-09-10 17:27 bmatschke with assisted by an agent values of erf(x) at rational arguments
2026-09-10 17:26 bmatschke the erf alone, with its own parameters
2026-09-10 17:22 bmatschke with assisted by an agent values of erf(x) at rational arguments
2026-09-10 14:47 zeta3 clarify definitions and related-function prose
2026-09-10 14:44 zeta3 clarify definitions and related-function prose
2026-09-10 14:17 zeta3 shortened the definition after audit
2026-09-10 14:12 zeta3 error function family values at rational arguments
2026-09-10 14:10 zeta3 drafted the error function family table

What changed between 2026-09-11 09:00 and 2026-09-11 09:18

from line 125 (6 lines) @@ -125,6 +125,6 @@
   rigour: proven   complete: 'no'-  complete-note: it holds $\operatorname{erf}(x)$ at every rational $x=a/b$ in lowest-    terms with $b\leq18$ and $0\leq x\leq10$+  complete-note: it holds $\operatorname{erf}(x)$ at every $x$ of two decimal places+    with $0\leq x\leq10$   rigour details: Each value was computed as a ball with arb at `numberdb.bits(digits,     losing=64)` bits, and checked against mpmath at 150 decimal digits, against the
from line 135 (1003 lines, 2002 fewer than before) @@ -135,3005 +135,1003 @@
   number-header: $\operatorname{erf}(x)$ Numbers:-- params:-    x: '0'-  number: '0'-- params:-    x: 1/100-  number: '0.01128341555584961691590952354806921094910095483011645227700648545172867371923837433659144582754544789'-- params:-    x: 1/50-  number: '0.02256457469184494422436586164740763980744316304134269234713788775598755146294564967487754873416406251'-- params:-    x: 3/100-  number: '0.03384122234173543330221665425687546522573391212059352761271413510228148862691122838856663411013894483'-- params:-    x: 1/25-  number: '0.04511110614512475208974906472922758576507467850233615121308732072451203968631542195307603338905383561'-- params:-    x: 1/20-  number: '0.05637197779701662383127111260203294529117300589267344119273562471188327147471635625239040177835714023'-- params:-    x: 3/50-  number: '0.06762159439330844207943145239124403339529636663259073851707318518991697376964676702159417921004321830'-- params:-    x: 7/100-  number: '0.07885771977089074335699703866798443882124089094977175334730330266636245696812441897990893458807849754'-- params:-    x: 2/25-  number: '0.09007812584101816072339218761611912831460673566139478223277382429372899540303609912475957914421617516'-- params:-    x: 9/100-  number: '0.1012805939146268833524981632441209898580123629456802604570183538530655994608563468929666299420431099'-- params:-    x: 1/10-  number: '0.1124629160182848922032750717439683832216962991597025475344941448175992440255313591702211741364051969'-- params:-    x: 11/100-  number: '0.1236228961994743097698385626280168657744254434649864928080061019691820107691074454069458129825913081'-- params:-    x: 3/25-  number: '0.1347583518199200692950141260580204707041366222575618968311650337806107795874974675614994143305282128'-- params:-    x: 13/100-  number: '0.1458671148356957490829576088953245695665867661475508323219585957530959616291386154036221028988602103'-- params:-    x: 7/50-  number: '0.1569470330628558008719022464756233931148761258488869609339023098357103434298365021078951186149587959'-- params:-    x: 3/20-  number: '0.1679959714273634947702095223814588196046831893377416239144383083725948064948503080082155422763848432'-- params:-    x: 4/25-  number: '0.1790118131981056711551837282869479491368888537022547515721879002296488150828537599270466040272730157'-- params:-    x: 17/100-  number: '0.1899924612018087933950819859311985917254713548396009887055483757042016742083705037559833839729605623'-- params:-    x: 9/50-  number: '0.2009358390186957926484127106222833640405508464479355228956451269192568624967239713967063032795184474'-- params:-    x: 19/100-  number: '0.2118398921577497429369472489881767042426365640120445136239950671200652463362872536664835832937077166'-- params:-    x: 1/5-  number: '0.2227025892104784541401390068001438163882690384302276056209350238883636742719121828703537237787407004'-- params:-    x: 21/100-  number: '0.2335219229821035729252630004211367817707636978961832185859068350779353807725677088855124771330212864'-- params:-    x: 11/50-  number: '0.2442959115991286848692616942611377911277691540758209551489849106256012429879674095093666744340922061'-- params:-    x: 23/100-  number: '0.2550225995922731607701785272627287336352847806365818340735067482357080170079781995873859459201885929'-- params:-    x: 6/25-  number: '0.2657000589537920297957120900254244378064907322934200005092308374590342350878876022116992286476033015'-- params:-    x: 1/4-  number: '0.2763263901682369329850682677648157120653539778923112540824719312626850838973022251851848058497413668'-- params:-    x: 13/50-  number: '0.2868997232157491520483320553692229539848022383964621890900637170700016068708735456696629421963805933'-- params:-    x: 27/100-  number: '0.2974182185470127578938819424358648173150966466924635840321253957344255691149828305388647683678405925'-- params:-    x: 7/25-  number: '0.3078800680290340166489995995722447529786162635031214712584682836689859013927899086418199024382268464'-- params:-    x: 29/100-  number: '0.3182834958609522623389919483811033373694732632935628824073991647066386659387616868080031274326381366'-- params:-    x: 3/10-  number: '0.3286267594591274276389140478667565511699180962626758226091431398537105798906180858953222226974787062'-- params:-    x: 31/100-  number: '0.3389081503107902486994993648159052518457616477100725793861462897760540646176030110862649608941684913'-- params:-    x: 8/25-  number: '0.3491259947955827573156946332417304660499009511985427008906834693860275100009850598434922727591924590'-- params:-    x: 33/100-  number: '0.3592786549743589729882539533575186226801213574668743356583371521758169829570452794685256800880954962'-- params:-    x: 17/50-  number: '0.3693645293446586372041239969721059908182425978112591715050864449302001310791175155535706944080000180'-- params:-    x: 7/20-  number: '0.3793820535623103202972999836194563114266284583836991320591688105207318713161767932919971279157068502'-- params:-    x: 9/25-  number: '0.3893297011286642047536284505503976753097780503125673494673872052460138465688897101647448305965926252'-- params:-    x: 37/100-  number: '0.3992059840429992345821437102027271869779330600622908159342517515176075918212756164121887208724181587'-- params:-    x: 19/50-  number: '0.4090094534196940449182391286758218150599858169212497184264038199912807921255174324794271362138801034'-- params:-    x: 39/100-  number: '0.4187387000697960757595577821694256947482790565607176555293235109299044935242474628082823877880095054'-- params:-    x: 2/5-  number: '0.4283923550466684551036038453201724441218629285225903834950863461133333685056718024227261581105386271'-- params:-    x: 41/100-  number: '0.4379690901554395363731300972832062099187698338527251166875649721045891983046884930592521539318082745'-- params:-    x: 21/50-  number: '0.4474676184260253198194105938973533000559435609693234075062632399949536380906002517489444159532438888'-- params:-    x: 43/100-  number: '0.4568866945495403049874420036700847312376101286503599577022501603633420177848251017407232190694555930'-- params:-    x: 11/25-  number: '0.4662251152779575393197046433772817370406354043153667747713130062981765205167662673186612896147410101'-- params:-    x: 9/20-  number: '0.4754817197869236753196815254595079821972956712348994132614927874036127787624800512357936830224169124'-- params:-    x: 23/50-  number: '0.4846553900016796550267031225717793865128918168273141866157941249324560960116037106942077945565626713'-- params:-    x: 47/100-  number: '0.4937450508860821365170915968985935168123649734287445205717162013382605264570696146233036981904627844'-- params:-    x: 12/25-  number: '0.5027496706947648945332662286283985243254240819292256909443426643246912497142355555102649284235004473'-- params:-    x: 49/100-  number: '0.5116682611885230992116967083860786431210987706011659959567177868612733816800627677132880952152221050'-- params:-    x: 1/2-  number: '0.5204998778130465376827466538919645287364515757579637000588057256471935217168535709147882187347877570'-- params:-    x: 51/100-  number: '0.5292436198411704290100703122388392977176907860254549133093325711124765530227755711448010259646034562'-- params:-    x: 13/25-  number: '0.5378986304788544311066144133890206812942603005225209640006674354743279844487974598572149268250610742'-- params:-    x: 53/100-  number: '0.5464640969351416882225326724552485345722613568159163993225501962033969582170861729163758028139940660'-- params:-    x: 27/50-  number: '0.5549392504563902604975394942240392127047994946642246497455846902628897002885317578535806903879363650'-- params:-    x: 11/20-  number: '0.5633233663251089559916883635568262739438498364139102862781996203797796069872764948290032850368583783'-- params:-    x: 14/25-  number: 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'0.6270464433381956904647362605565403783398585472633722434515933233760620459089898469182563471631831685'-- params:-    x: 16/25-  number: '0.6345858291221413138597056944538145418525253916201453375740771485627026378819945141039430283118510587'-- params:-    x: 13/20-  number: '0.6420293273556718412929464663308366308772614566660360203938861397386189916903234049771796210098791878'-- params:-    x: 33/50-  number: '0.6493766879629542227502750119250159317352038091916685693144159372092688709878545628692152771750545675'-- params:-    x: 67/100-  number: '0.6566277023003050464390844632819999594167262075715792123582825394198315505448167987229782706695970668'-- params:-    x: 17/25-  number: '0.6637822027413579854248676989151846371650913583619553993868701984904183373380406110249329617334414474'-- params:-    x: 69/100-  number: '0.6708400622350777843568868125317943326434326800342212680349185600838748610585556211781684034522866495'-- params:-    x: 7/10-  number: 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