cp's OEIS Frontend

A257959 Decimal expansion of the Digamma function at 1/2 + 1/Pi, negated.

%I A257959 #8 May 28 2015 08:24:22
%S A257959 9,2,3,6,3,2,6,7,5,9,6,1,3,3,7,7,3,4,6,0,0,0,2,6,3,3,4,7,4,8,6,7,4,7,
%T A257959 1,3,9,8,9,4,8,9,3,2,1,5,2,6,1,0,2,7,5,3,8,5,3,5,3,9,9,3,1,5,7,2,2,0,
%U A257959 1,3,8,9,5,4,1,0,3,9,8,8,6,7,3,3,8,7,7,1,3,7,8,2,8,0,9,1,7,3,1,0,8,9,4
%N A257959 Decimal expansion of the Digamma function at 1/2 + 1/Pi, negated.
%C A257959 The reference gives an interesting series representation with rational coefficients for Psi(1/2 + 1/Pi) = -log(Pi) + 1/4 + 1/16 - 5/576 - 13/512 - 569/25600 -539/36864 - 98671/12042240 - 16231/3932160 - ...
%H A257959 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.
%e A257959 -0.9236326759613377346000263347486747139894893215261027...
%p A257959 evalf(Psi(1/2+1/Pi), 120);
%t A257959 RealDigits[PolyGamma[1/2+1/Pi], 10, 120][[1]]
%o A257959 (PARI) default(realprecision, 120); psi(1/2+1/Pi)
%Y A257959 Cf. A257955, A257957, A257958, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.
%K A257959 nonn,cons
%O A257959 0,1
%A A257959 _Iaroslav V. Blagouchine_, May 14 2015