History of 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'+Comments:+  comment-Riemann-zeta-definition: The Riemann zeta function $\zeta(s)$ is the meromorphic+    continuation of the Dirichlet series  $\sum_{n=0}^\infty n^{-s}, \Re(s) > 1$.+  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).+Programs:+  program-sage:+    language: Sage+    code: 's = var("s")++      xi(s) = 1/2 * s*(s-1)*pi^(-s/2)*gamma(s/2)*zeta(s)++      numbers = {n: xi.derivative(s,n)(s=1/2) for n in [0..10]}'+References:+  Kei92:+    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+    MR: '1122072'+Links:+  WikiZeta:+    title: 'Wikipedia: Riemann zeta function'+    url: https://en.wikipedia.org/wiki/Riemann_zeta_function+  WikiXi:+    title: 'Wikipedia: Riemann Xi function'+    url: https://en.wikipedia.org/wiki/Riemann_Xi_function+Similar tables: ''+Keywords: ''+Tags:+- Taylor series+- L-function+Data properties:+  type: R+  complete: 'no'+Numbers:+  a_n:+    param-latex: $a_n$+    numbers:+      '0': '0.497120778188314109912773739685397719807293609557705185933234233998495529045543485239169964978388143'+      '1': '0'+      '2': '0.022971944315145437535249876497632170264593013837589063499144622165183631858892553809670227671214178'+      '3': '0'+      '4': '0.002962848433687632165368298995876427315263843916359126935030665429364981704168657743383689954024840'+      '5': '0'+      '6': '0.000599295946597579491843426282608126906610908976152441453825466312648624918331709362016197982712905'+      '7': '0'+      '8': '0.000160966574550195610884922897005445160054659884764504055352339242290836298973885415252234568011432'+      '9': '0'+      '10': '0.000053038634278290654777521183707488595689757588872269938618371957816641081083250360933546158345197'+      '11': '0'+      '12': '0.000020475115210762215936783578983840568947868798970635291025613749309896375187468972006201018320409'+      '13': '0'+      '14': '8.987755893268589762760726109431665626492479706408592808899025568357431904916947449361315236295212784e-6'+      '15': '0'+      '16': '4.393304250907866014151292100883561819319459231926712365498452902910009249027438410555498710809721935e-6'+      '17': '0'+      '18': '2.354883383579171151030545408592339785927954828705767066636099019744053975733021029833014458013773424e-6'+      '19': '0'+      '20': '1.367986151588876149236144977047514117335483346162041407436104104812636794539850554854732180293820871e-6'+      '21': '0'+      '22': '8.533143911690811533977450810335954707366522596463622625974585044845271925522739163266328628267593385e-7'+      '23': '0'+      '24': '5.672972475787218476150681068689488439218075414981540601164513110113083381981466277094723741374373462e-7'+      '25': '0'+      '26': '3.995048218196427002173490709241001490040910331553287772939869728860167177539762614722647300724625471e-7'+      '27': '0'+      '28': '2.964945682660373093507964168428032521349100689298744461733732362167880339649982616932860991002166530e-7'+      '29': '0'+      '30': '2.308919955117118068707683409955140507520452074191960053696176341161239766651435997546620146241528763e-7'+  a_n/n!:+    param-latex: $a_n/n!$+    numbers:+      '0':+        'equals:': HREF{#a_n,0}+        'number:': '0.497120778188314109912773739685397719807293609557705185933234233998495529045543485239169964978388143'+      '1': '0'+      '2': '0.011485972157572718767624938248816085132296506918794531749572311082591815929446276904835113835607089'+      '3': '0'+      '4': '0.000123452018070318006890345791494851138135993496514963622292944392890207571007027405974320414751035'+      '5': '0'+      '6': '8.323554813855270720047587258446207036262624668783909080909254342342012754607074472447194204345907472e-7'+      '7': '0'+      '8': '3.992226551344137174725270263031874009292159840389485499810001048879868526138031132247881151077199149e-9'+      '9': '0'+      '10': '1.461602576011096086241214277653455569051961774478338255576828643536184994578107389041726144874282723e-11'+      '11': '0'+      '12': '4.274540045536844957675210058555246777436400832614189811811432218576383708837083635253205484159072397e-14'+      '13': '0'+      '14': '1.030962613461800655569712074080165685387106980414017659582093938583351345262081421637376076063212946e-16'+      '15': '0'+      '16': '2.099769808149528750910377684371822249462843352110573164065056496021153012798174695580778328948691460e-19'+      '17': '0'+      '18': '3.678141095500770177672859444023590651059999986846439585634400605345278906464402838919266008919188604e-22'+      '19': '0'+      '20': '5.622857587322744290380297231857258375167392825889289087058025488623970227364770808140830260430370961e-25'+      '21': '0'+      '22': '7.591760130407282691957677231234202446737092631085165174605224139684839070733461831915634939605449689e-28'+      '23': '0'+      '24': '9.143342879020424568168879288216860580041093069354086566869468132446371504542087795368504129281289082e-31'+      '25': '0'+      '26': '9.906106633242745686869166090768423371272702090946843324625856279628600924573371919725187300173955101e-34'+      '27': '0'+      '28': '9.724693433054440845992485409457861854198454055480374068007129469481152574832664382441452293254966172e-37'+      '29': '0'+      '30': '8.704599666717711232627911292940822517823662219846333387337426642911642235221720629001009783630786909e-40'