A020777 Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where Gamma(x) denotes the Gamma function.

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

Offset: 1

Author

Benoit Cloitre, May 24 2003

Keywords

• cons
• nonn

Examples

			4.2274535333762654080895301460966835773672444387082422716552795595189567958...
		

References

• S.J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135, 1995.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• E. D. Krupnikov, K. S. Kölbig, Some special cases of the generalized hypergeometric function (q+1)Fq, J. Comp. Appl. Math. 78 (1997) 79-95, psi(1/4).
• Wikipedia, Digamma function
• Index entries for sequences related to the digamma function

Crossrefs

Cf. A001620, A200134, A301816.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R) + Pi(R)/2 + Log(8); // G. C. Greubel, Aug 28 2018

Maple

evalf(gamma+3*log(2)+Pi/2) ; # R. J. Mathar, Nov 13 2011
evalf(abs(Psi(1/4))) ; # R. J. Mathar, Nov 19 2024

Mathematica

EulerGamma + Pi/2 + Log[8] // RealDigits[#, 10, 105][[1]] & (* Jean-François Alcover, Jun 18 2013 *)
N[StieltjesGamma[0, 1/4], 99] (* Peter Luschny, May 16 2018 *)

PARI

Euler+3*log(2)+Pi/2

Formula

Gamma'(1/4)/Gamma(1/4) = -EulerGamma - 3*log(2) - Pi/2 where EulerGamma is the Euler-Mascheroni constant (A001620).

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