A114875 Decimal expansion of -zeta'(1/2).

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

Offset

1,1

Links

Table of n, a(n) for n=1..102.

B. K. Choudhury, The Riemann zeta-function and its derivatives, Proc. R. Soc. Lond. A 445 (1995) 477, Table 3.

J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function.

Formula

Equals ((2*gamma + Pi + 2*log(8*Pi))*zeta(1/2))/4, where gamma is Euler's constant (A001620).

Example

3.92264613920915172747153144671459951373032397150650...

Maple

Zeta(1, 1/2) ; evalf(%) ; # R. J. Mathar, May 03 2021

Mathematica

RealDigits[-Zeta'[1/2], 10, 120][[1]] (* Amiram Eldar, Jun 15 2023 *)

Prog

(PARI) -zeta'(1/2) \\ Charles R Greathouse IV, Mar 28 2012
(PARI) -(2*Euler+Pi+2*log(8*Pi))*zeta(1/2)/4 \\ Charles R Greathouse IV, Mar 28 2012

Crossrefs

Cf. A001620, A059750.

Sequence in context: A229099 A021259 A194807 * A275371 A225357 A201664

Adjacent sequences: A114872 A114873 A114874 * A114876 A114877 A114878

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 03 2006

Status

approved