A020759 Decimal expansion of (-1)*Gamma'(1/2)/Gamma(1/2) where Gamma(x) denotes the Gamma function.

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

Offset: 1

Author

Benoit Cloitre, May 24 2003

Keywords

• cons
• nonn

Comments

Decimal expansion of -psi(1/2). - Benoit Cloitre, Mar 07 2004

Examples

			1.96351002602142347944097633299875556719315960466...
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), 6.3.3, p. 258. - Robert G. Wilson v, Jun 20 2011
• S. J. Patterson, An introduction to the theory of the Riemann zeta function, Cambridge studies in advanced mathematics no. 14, p. 135.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Wikipedia, Digamma function.
• Index entries for sequences related to the digamma function.

Crossrefs

Cf. A001620, A002161, A002162, A131265, A248176.

Programs

Magma

R:=RealField(100); EulerGamma(R) + 2*Log(2); // G. C. Greubel, Aug 27 2018

Maple

evalf(-Psi(0.5)) ; # R. J. Mathar, Sep 10 2013

Mathematica

RealDigits[ EulerGamma + 2 Log[2], 10, 111][[1]] (* Robert G. Wilson v, Jun 20 2011 *)

PARI

Euler+2*log(2)

PARI

2-psi(-1/2) \\ Stanislav Sykora, Oct 03 2014

Formula

Gamma'(1/2)/Gamma(1/2) = -EulerGamma - 2*log(2) = -1.9635100260214234794... where EulerGamma is the Euler-Mascheroni constant (A001620).

Equals 2 - psi(-1/2) = 2-A248176. - Stanislav Sykora, Oct 03 2014

Equals A131265/A002161. - R. J. Mathar, Jun 02 2022

Equals lim_{n->oo} (Sum_{k=0..n} 1/(k+1/2) - log(n)). - Amiram Eldar, Mar 04 2023