OFFSET
0,1
LINKS
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
KEYWORD
dead
AUTHOR
Jean-François Alcover, Sep 17 2014
STATUS
approved