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A255695 Decimal expansion of the Plouffe sum S(1,1) = Sum_{n >= 0} 1/(n*(exp(Pi*n)-1)). 8
4, 6, 1, 2, 8, 9, 7, 8, 7, 7, 9, 3, 5, 0, 1, 0, 0, 7, 0, 7, 7, 6, 1, 3, 7, 1, 9, 3, 4, 3, 3, 5, 2, 8, 1, 3, 6, 7, 9, 4, 0, 7, 7, 0, 4, 9, 8, 2, 1, 7, 0, 6, 6, 2, 8, 3, 5, 3, 5, 9, 3, 1, 3, 6, 4, 0, 3, 5, 8, 0, 0, 3, 6, 6, 1, 4, 4, 8, 9, 1, 5, 0, 0, 6, 0, 5, 9, 2, 9, 6, 8, 8, 2, 8, 1, 5, 5, 5, 0, 2, 3, 0, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-1,1

LINKS

Table of n, a(n) for n=-1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 5.

Simon Plouffe, Identities inspired by Ramanujan Notebooks (part 2), April 2006

Linas Vepštas, On Plouffe’s Ramanujan Identities, arXiv:math/0609775 [math.NT]

FORMULA

This is the case k = m = 1 of S(k,m) = Sum_{n >= 0} 1/(n^k*(exp(m*Pi*n)-1)).

Pi = 72*S(1,1) - 96*S(1,2) + 24*S(1,4).

EXAMPLE

0.046128978779350100707761371934335281367940770498217...

MATHEMATICA

digits = 104; S[1, 1] = NSum[1/(n*(Exp[Pi*n] - 1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> digits]; RealDigits[S[1, 1], 10, digits] // First

CROSSREFS

Cf. A255696 (S(1,2)), A255697 (S(1,4)), A255698 (S(3,1)), A255699 (S(3,2)), A255700 (S(3,4)), A255701 (S(5,1)), A255702 (S(5,2)), A255703 (S(5,4)),

Sequence in context: A248938 A106144 A154478 * A246489 A343624 A309445

Adjacent sequences:  A255692 A255693 A255694 * A255696 A255697 A255698

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Mar 02 2015

STATUS

approved

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Last modified June 17 05:25 EDT 2021. Contains 345080 sequences. (Running on oeis4.)