A248176 Decimal expansion of psi(-1/2).

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

Offset

0,2

Comments

Psi denotes the digamma function.

Links

Stanislav Sykora, Table of n, a(n) for n = -1..2000

Wikipedia, Digamma function.

Formula

Equals 2 + psi(1/2) = 2 - 2*log(2) - EulerGamma = 2 - A020759, (since psi(1 + x) = psi(x) + 1/x).

Equals PolyGamma(3/2). - Peter Luschny, Apr 14 2020

Equals Sum_{k>=1} (zeta(2*k+1)-1)/((k+1)*(2*k+1)). - Amiram Eldar, May 24 2021

Equals 4*Pi*Integral_{x>=0} (log(1 + i*x) / (exp(-Pi*x) + exp(Pi*x))^2). - Peter Luschny, Aug 04 2021

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

Example

0.0364899739785765205590236670012444328068403953395658929528727461...

Mathematica

RealDigits[2 - (EulerGamma + 2Log[2]), 10, 100][[1]] (* Alonso del Arte, Oct 03 2014 *)

Prog

(PARI) psi(-1/2)
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2 - (2*Log(2) + EulerGamma(R)); // G. C. Greubel, Aug 30 2018

Crossrefs

Cf. A001620, A002162, A020759.

Sequence in context: A004546 A197255 A154890 * A100000 A083682 A021278

Adjacent sequences: A248173 A248174 A248175 * A248177 A248178 A248179

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Oct 03 2014

Status

approved