A222457 - OEIS

%I #23 Aug 27 2024 06:50:58

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

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

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

%N Decimal expansion of the negated value of the digamma function at 1/6.

%H Vincenzo Librandi, <a href="/A222457/b222457.txt">Table of n, a(n) for n = 1..5000</a>

%H Ernst D. Krupnikov and K. S. Kolbig, <a href="https://doi.org/10.1016/S0377-0427(96)00111-2">Some special cases of the generalized hypergeometric function _{q+1}F_q</a>, J. Comp. Appl. Math. 78 (1997) 79-95

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GausssDigammaTheorem.html">Gauss's Digamma Theorem</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function#Special_values">Digamma function: special values</a>.

%H <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a>

%F Psi(1/6) = -gamma -Pi*sqrt(3)/2 -3*log(3)/2 -2*log(2).

%e Psi(1/6) = -6.3321275053749147924249615748457777225904948...

%t RealDigits[-PolyGamma[1/6], 10, 90][[1]]

%o (PARI) -psi(1/6)

%o (Maxima) fpprec:90; ev(bfloat(-psi[0](1/6)));

%Y Cf. A020759, A047787, A200064, A222458.

%K nonn,cons

%O 1,1

%A _Bruno Berselli_, Feb 21 2013