Mathematical constants and numbers
edited bySimon PlouffeAssociate ProfessorLaCIM, University of Quebec at Montrealhttp://www.lacim.uqam.ca/pi : Plouffe's Inverterplouffe@math.uqam.ca
The value of Zeta(3) to 1,000,000 decimal digits.the number is defined as sum(1/n^3,n=1..infinity), thesum of inverses of cubes and equals 1.2020569031…
Computed by : Sebastian Wedeniwski (wedeniws@de.ibm.com)who computed more than 128 million digits using this moreefficient formula found by Theodor Amdeberhan and Doron Zeilberger.
/ \
| ——— 3 |
| \ n A(n) ((2 n + 1)! (2 n)! n!) |
Zeta(3) = 1/24 | ) (-1) ——————————————— |
| / 3 |
| ——— (3 n + 2)! ((4 n + 3)!) |
\ n >= 0 /
5 4 3 2with A(n) := 126392 n + 412708 n + 531578 n + 336367 n + 104000 n + 12463given by Theodor Amdeberhan and Doron Zeilberger (see [1]).
References:===========
[1] T. Amdeberhan und D. Zeilberger: Hypergeometric Series Acceleration via
the WZ Method, Electronic Journal of Combinatorics (Wilf Festschrift
Volume) 4 (1997).
[2] B. Haible, T. Papanikolaou: Fast multiprecision evaluation of series of
rational numbers, Technical Report TI-97-7, Darmstadt University of
Technology, April 1997.
[3] S. Wedeniwski: Piologie - Eine exakte arithmetische Bibliothek in C++, Technical Report WSI 96-35, Tuebingen University, available by anonymous ftp from "ftp://ftp.informatik.uni-tuebingen.de/pub/CA/software/Piologie/" or "ftp://ruediger.informatik.uni-tuebingen.de/Piologie/".
1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915779526071941849199599867328321377639683720790016145394178294936006671919157552224249424396156390966410329115909578096551465127991840510571525598801543710978110203982753256678760352233698494166181105701471577863949973752378527793703095602570185318279000307654710756304884332086971157374238079344503160762531771453544441183117818224971852635709182448998796203508335756172022603393785870328131267807990054177348691152537065623705744096622171290262732073236149224291304052855537234103307757779806424202430488281521000914602653822069627155202082274335001015294801198690117625951676366998171835575234880703719555742347294083595208861666202572853755813079282586487282173705566196898952662018776810629200817792338135876828426412432431480282173674506720693507626895304345939375032966363775750624733239923482883107733905276802007579843567937115050900502736604711400853350343646722485653151811776618109222791910224883968002666065687051906275973877353574444787753791641427381322569573196020187488474710469933656614008069303256185371886007271853594828847886245041855546408571556300712509027138634689374168266546657729261117182460363056604653004752217032651363910586988578842450413400076174727913718427741087508679050188965396356958643081961372990232749349702416226454339239292672783678655715558177739663771912814182246641268663452811055140131673253668418279295372660503415185270488028902683158334795920387559849886178670059637310157271720001143347673515418825525246632629