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

1,2

Comments

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

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.

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

Example

1.96351002602142347944097633299875556719315960466...

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 *)

Prog

(PARI) Euler+2*log(2)
(PARI) 2-psi(-1/2) \\ Stanislav Sykora, Oct 03 2014
(Magma) R:=RealField(100); EulerGamma(R) + 2*Log(2); // G. C. Greubel, Aug 27 2018

Crossrefs

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

Sequence in context: A198997 A271172 A019683 * A226582 A276538 A243313

Adjacent sequences: A020756 A020757 A020758 * A020760 A020761 A020762

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2003

Status

approved