OFFSET
-5,1
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022, p. 6.
Simon Plouffe, Identities inspired by Ramanujan Notebooks (part 2), April 2006.
Linas Vepštas, On Plouffe's Ramanujan identities, The Ramanujan Journal, Vol. 27 (2012), pp. 387-408; alternative link; arXiv preprint, arXiv:math/0609775 [math.NT], 2006-2010.
FORMULA
This is the case k=1, m=4 of S(k,m) = Sum_{n >= 1} 1/(n^k*(exp(m*Pi*n)-1)).
Pi = 72*S(1,1) - 96*S(1,2) + 24*S(1,4).
Equals Sum_{k>=1} sigma(k)/(k*exp(4*Pi*k)). - Amiram Eldar, Jun 05 2023
EXAMPLE
0.000003487360598600608547009753485704881044662756456465722...
MATHEMATICA
digits = 104; S[1, 4] = NSum[1/(n*(Exp[4*Pi*n] - 1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> digits]; RealDigits[S[1, 4], 10, digits] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Mar 02 2015
STATUS
approved