A257957 - OEIS

%I #11 May 28 2015 08:23:06

%S 1,0,3,3,6,4,6,1,2,5,7,6,5,5,8,2,7,0,6,4,8,5,5,3,7,4,5,5,3,3,1,6,1,7,

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

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

%N Decimal expansion of log(Gamma(1/Pi)).

%C The reference gives an interesting series representation with rational coefficients for log(Gamma(1/Pi)) = (1-1/Pi)*log(Pi) - 1/Pi + log(2)/2 + (1 + 1/4 + 1/12 + 1/32 + 1/75 + 1/144 + 13/2880 + 157/46080 + ...)/(2*Pi).

%C The value log(Gamma(1/Pi)) is also intimately related to integral_{x=0..1} arctan(arctanh(x))/x (A257963).

%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.

%e 1.0336461257655827064855374553316178667100308701595988...

%p evalf(log(GAMMA(1/Pi)), 120);

%t RealDigits[Log[Gamma[1/Pi]], 10, 120][[1]]

%o (PARI) default(realprecision, 120); log(gamma(1/Pi))

%Y Cf. A257955, A257963, A257958, A257959, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.

%K nonn,cons

%O 1,3

%A _Iaroslav V. Blagouchine_, May 14 2015