A375772 Decimal expansion of the absolute value of the second derivative of the digamma function at 3/4.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Ernst D. Krupnikov and K. S. Kolbig, Some special cases of the generalized hypergeometric function _{q+1}F_q, J. Comp. Appl. Math. 78 (1997) 79-95.

Formula

psi''(3/4) = 2*(Pi^3-28*zeta(3)) = 2*(4/3)^3 * 4F3(3/4,3/4,3/4,1 ; 7/4,7/4,7/4;1).

Example

psi''(3/4) = -5.3026332163376396314327...

Maple

2*(Pi^3-28*Zeta(3)); evalf(%) ;

Mathematica

RealDigits[PolyGamma[2, 3/4], 10, 105][[1]] (* Vaclav Kotesovec, Aug 27 2024 *)

Prog

(PARI) 2*zetahurwitz(3, 3/4) \\ Charles R Greathouse IV, Jul 08 2026

Crossrefs

Cf. A200134 (psi(3/4)), A282824 (psi'(3/4)).

Sequence in context: A077602 A238008 A375837 * A193547 A144481 A374172

Adjacent sequences: A375769 A375770 A375771 * A375773 A375774 A375775

Keyword

nonn,cons

Author

R. J. Mathar, Aug 27 2024

Status

approved