|
%I #13 Aug 14 2023 08:43:26
%S 3,2,9,0,2,1,3,9,6,0,1,7,3,2,2,4,0,9,0,8,4,3,0,9,0,8,4,5,5,4,0,0,1,9,
%T 0,3,7,4,0,2,1,9,3,2,8,2,0,0,7,0,1,6,1,2,9,3,8,8,9,5,3,1,8,3,7,5,5,3,
%U 7,5,6,6,5,3,3,7,1,7,9,1,2,9,1,5,3,2,8,7,7,1,1,1,6,9,3,5,6,7,3,1,6,6,9
%N Decimal expansion of the Digamma function at 1/Pi, negated.
%C 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 + ...
%H Iaroslav V. Blagouchine, <a href="http://arxiv.org/abs/1408.3902">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</a>, Mathematics of Computation (AMS), 2015.
%F 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
%e -3.2902139601732240908430908455400190374021932820070161...
%p evalf(Psi(1/Pi), 120);
%t RealDigits[PolyGamma[1/Pi], 10, 120][[1]]
%o (PARI) default(realprecision, 120); psi(1/Pi)
%Y Cf. A257955, A257957, A257959, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.
%K nonn,cons
%O 1,1
%A _Iaroslav V. Blagouchine_, May 14 2015
|
