A245018 Duplicate of A241991

5, 4, 5, 7, 8, 1, 8, 3, 8, 8, 3, 3, 9, 8, 7, 0, 8, 2, 5, 2, 3, 4, 9, 0, 3, 9, 7, 2, 5, 5, 6, 5, 8, 7, 7, 4, 0, 3, 3, 6, 8, 7, 9, 1, 3, 2, 9, 8, 0, 4, 3, 9, 3, 2, 7, 6, 7, 5, 9, 5, 2, 6, 2, 3, 5, 0, 6, 1, 8, 4, 4, 6, 8, 7, 4, 1, 0, 8, 4, 0, 5, 2, 5, 1, 2, 7, 0, 3, 1, 0, 6, 0, 2, 6, 1, 0, 0, 3, 0, 6

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 3.

S. R. Holcombe, A product representation for Pi, arXiv:1204.2451 [math.NT], 2012.

Formula

exp(1/2 + 2*Pi/3 - zeta(3)/(2*Pi^2) + Li_3(e^(-2*Pi))/(2*Pi^2) + Li_2(e^(-2*Pi))/Pi)/(2*sinh(Pi)).

Example

0.545781838833987082523490397255658774033687913298...

Maple

evalf(product((1+1/n^2)^(n^2)/exp(1), n=1..infinity), 120) # Vaclav Kotesovec, Sep 17 2014

Mathematica

p = Exp[1/2 + 2*Pi/3 - Zeta[3]/(2*Pi^2) + PolyLog[3, E^(-2*Pi)]/(2*Pi^2) + PolyLog[2, E^(-2*Pi)]/Pi]/(2*Sinh[Pi]); RealDigits[p, 10, 100] // First

Prog

(Python)
from mpmath import *
mp.dps=101
C = exp(1/2 + 2*pi/3 - zeta(3)/(2*pi**2) + polylog(3, e**(-2*pi))/(2*pi**2) + polylog(2, e**(-2*pi))/pi)/(2*sinh(pi))
print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 03 2017

Crossrefs

Sequence in context: A069214 A119807 A254181 * A241991 A184306 A176317

Adjacent sequences: A245015 A245016 A245017 * A245019 A245020 A245021

Keyword

dead

Author

Jean-François Alcover, Sep 17 2014

Status

approved