A200134 - OEIS

%I #31 May 13 2024 21:05:47

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

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

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

%N Decimal expansion of the negated value of the digamma function at 3/4.

%H G. C. Greubel, <a href="/A200134/b200134.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%F Psi(3/4) = -gamma + Pi/2 - 3*log(2) = A000796 - A020777 = 3.14159... - 4.22745...

%F Pi = gamma(0,1/4) - gamma(0,3/4) = A020777 - A200134, where gamma(n,x) denotes the generalized Stieltjes constants. - _Peter Luschny_, May 16 2018

%e Psi(3/4) = -1.085860879786472169626886762817...

%p evalf(-gamma+Pi/2-3*log(2)) ;

%t RealDigits[ -PolyGamma[3/4], 10, 97] // First (* _Jean-François Alcover_, Feb 20 2013 *)

%t N[StieltjesGamma[0, 3/4], 99] (* _Peter Luschny_, May 16 2018 *)

%o (PARI) -psi(3/4) \\ _Charles R Greathouse IV_, Nov 22 2011

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); -EulerGamma(R) + Pi(R)/2 - 3*Log(2); // _G. C. Greubel_, Aug 29 2018

%Y Cf. A001620, A020759, A020777, A047787, A301816.

%K cons,nonn

%O 1,3

%A _R. J. Mathar_, Nov 13 2011