OFFSET
1,1
COMMENTS
The reference gives an interesting series representation with rational coefficients for Psi(1/Pi) = -log(Pi) - Pi/2 - 1/2 - 1/8 - 1/72 + 1/64 +7/400 + 7/576 + 643/94080 + 103/30720 + ...
LINKS
Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to 1/Pi, Mathematics of Computation (AMS), 2015.
FORMULA
Int_0^infinity x*dx/[(x^2+1)(exp(2x)-1)] = -Pi/2-Psi(1/Pi) = -1.5707...+ 3.2902.. = 1.71941... - R. J. Mathar, Aug 14 2023
EXAMPLE
-3.2902139601732240908430908455400190374021932820070161...
MAPLE
evalf(Psi(1/Pi), 120);
MATHEMATICA
RealDigits[PolyGamma[1/Pi], 10, 120][[1]]
PROG
(PARI) default(realprecision, 120); psi(1/Pi)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Iaroslav V. Blagouchine, May 14 2015
STATUS
approved