A390074 Decimal expansion of psi'''(1/4).

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

Offset

4,2

Comments

Decimal expansion of the third derivative of the digamma function at 1/4.

Links

Table of n, a(n) for n=4..114.

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

Index entries for sequences related to the digamma function

Formula

Equals 8*(Pi^4+96*A175572) = 6*4^4* 5F4(1/4,1/4,1/4,1/4,1 ; 5/4,5/4,5/4,5/4 ;1).

Example

1538.782144009188396022791243...

Maple

Psi(3, 1/4) ; evalf(%) ;

Mathematica

RealDigits[PolyGamma'''[1/4], 10, 111][[1]] (* Stefano Spezia, Oct 23 2025 *)

Prog

(PARI) psi'''(1/4) \\ Michel Marcus, Oct 23 2025

Crossrefs

Cf. A375771 (psi''(1/4)), A175572 (beta(4)).

Sequence in context: A237192 A161488 A010484 * A174930 A179452 A396078

Adjacent sequences: A390071 A390072 A390073 * A390075 A390076 A390077

Keyword

cons,nonn

Author

R. J. Mathar, Oct 23 2025

Status

approved