History of Taylor coefficients of the completed Riemann zeta function at 1/2

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when	who	what
2026-08-14 21:29	bmatschke	how well the digits are known: proven (interval or ball arithmetic only)	current
2026-08-13 22:04	bmatschke	how well the digits are known: proven (interval or ball arithmetic only)
2026-08-09 09:25	label hoist	moved the parameter labels onto the parameter they describe
2026-08-09 09:10	flattening	entries rewritten as records with named parameters
2026-08-09 08:33	data-repository import	the current state of the data repository	reviewed
2021-03-18 21:23	bmatschke	from the data repository, b9dcfad6
2021-03-05 18:37	bmatschke	from the data repository, 9553fc42
2021-03-04 21:20	bmatschke	from the data repository, 2b4306e5
2021-03-04 19:49	bmatschke	from the data repository, 7c8d1063
2021-03-04 12:26	bmatschke	from the data repository, 78781344

What changed between 2021-03-04 12:26 and 2021-03-04 19:49

from line 1 (14 lines) @@ -1,14 +1,14 @@

-Title: Taylor coefficients of the completed Riemann zeta function at $1/2$.+Title: Taylor coefficients of the completed Riemann zeta function at 1/2. Definition: The list contains the coefficients of the Taylor expansion $\xi(s) = \sum_{n=0}^\infty   \frac{a_n}{n!} (s-1/2)^n$ of the completed Riemann zeta function $\xi(s) = \frac{1}{2}s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$   at $s=1/2$. Parameters:-  n:-    type: Z-    constraints: $n \neq 0$   expression:     title: Transformation of constant     type: Symbolic     show-in-parameter-list: 'no'+  n:+    type: Z+    constraints: $n \neq 0$ Comments:   comment-Riemann-zeta-definition: The Riemann zeta function $\zeta(s)$ is the meromorphic

from line 16 (5 lines) @@ -16,5 +16,5 @@

   comment-odd-coefficients: $a_n = 0$ for every odd $n$ due to CITE{formula-functional-equation}. Formulas:-  formula-functional-equation: $\xi(s) = xi(1-s)$ (functional equation).+  formula-functional-equation: $\xi(s) = \xi(1-s)$ (functional equation). Programs:   program-sage:

from line 27 (5 lines) @@ -27,5 +27,5 @@

 References:   Kei92:-    bib: J B. Keiper, "Power series expansions of Riemann's $\xi$ function", Math.+    bib: J. B. Keiper, "Power series expansions of Riemann's $\xi$ function", Math.       Comp. 58 (1992), 765-773.     doi: 10.1090/S0025-5718-1992-1122072-5

from line 46 (6 lines, 2 more than before) @@ -46,4 +46,6 @@

   type: R   complete: 'no'+Display properties:+  number-header: $n$<sup>th</sup> coefficient Numbers:   a_n:

from line 83 (30 lines, 20 more than before) @@ -81,10 +83,30 @@

       '29': '0'       '30': '2.308919955117118068707683409955140507520452074191960053696176341161239766651435997546620146241528763e-7'+      '31': '0'+      '32': '1.879671610622920268943772969212298732552589280732694925396131922958529118575058429301385187296865574e-7'+      '33': '0'+      '34': '1.594543628979342662694767268991018790425214135876973197052206455279213285720729343318207748937402176e-7'+      '35': '0'+      '36': '1.405559916949465441125714136062243508770778244992223276826515925510026540106904350106573355842319570e-7'+      '37': '0'+      '38': '1.284233905037717731618858419850508361014856859445414058276643798507288242721711404689022942782982399e-7'+      '39': '0'+      '40': '1.213573092303492609815783297604031019787259427223628876832155266350860859228708138499235403511791475e-7'+      '41': '0'+      '42': '1.183757713458838851377687502462867713884162132387436664248845459695707009341039130674770944507286885e-7'+      '43': '0'+      '44': '1.189789819582490268207615340693042429820464577030533947204854437722062494021553782589094435354084167e-7'+      '45': '0'+      '46': '1.230264872411736137782282963841505549027496496615708946117885346266819706304967320025436541310341873e-7'+      '47': '0'+      '48': '1.306841880695381644945425707320803500844753671055189568805897407668867008859680048008338748479113964e-7'+      '49': '0'+      '50': '1.424212569277436918033137935344978611835317927491394833494136717071030904121452486069053174338808212e-7'   a_n/n!:     param-latex: $a_n/n!$     numbers:       '0':-        'equals:': HREF{#a_n,0}-        'number:': '0.497120778188314109912773739685397719807293609557705185933234233998495529045543485239169964978388143'+        equals: HREF{#a_n,0}+        number: '0.497120778188314109912773739685397719807293609557705185933234233998495529045543485239169964978388143'       '1': '0'       '2': '0.011485972157572718767624938248816085132296506918794531749572311082591815929446276904835113835607089'

from line 139 (22 lines, 20 more than before) @@ -117,2 +139,22 @@

       '29': '0'       '30': '8.704599666717711232627911292940822517823662219846333387337426642911642235221720629001009783630786909e-40'+      '31': '0'+      '32': '7.143486611174271635933274689503696544914239871471640820244305998509524427808837627262335837584294900e-43'+      '33': '0'+      '34': '5.400970468614640162463535681258565756116701507659161328706157572851746992345928361111260553202408888e-46'+      '35': '0'+      '36': '3.778454654223714512573736764513978974957957043626396232833367571659848380135625616104163671509717817e-49'+      '37': '0'+      '38': '2.455407973097311854005859941599860939119077486172729690015218642132944146384988345211204709183345474e-52'+      '39': '0'+      '40': '1.487376345584122835490782580602367905855875187178309948322422043693646758103872642043021778834940260e-55'+      '41': '0'+      '42': '8.425285117990102465117906243494965439921278738074413642520693741215531277068454305498299034920851892e-59'+      '43': '0'+      '44': '4.475802362959008123898470468734532303453986445317795849290050575579705190194227570670101066164635541e-62'+      '45': '0'+      '46': '2.235779300633916142646417596315090927536933607059226301132906206385066290095085340411303022827305797e-65'+      '47': '0'+      '48': '1.052723349819719011960662642578145773874427942777236779730075908008523482516235903250888831830646010e-68'+      '49': '0'+      '50': '4.682738886317359934029750122962610730236541772733480195042695682806250457067279070502227902251065829e-72'