A390073 Decimal expansion of the negated value of psi''(1/3).

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

Offset

2,1

Comments

Decimal expansion of the absolute value of the second derivative of the digamma function at 1/3.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

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 26*Zeta(3)+4/9*sqrt(3)*Pi^3 = 2*3^3*A377557.

Example

psi''(1/3) = -55.1221223994016075524557559548150185690841906260...

Maple

Psi(2, 1/3) ; evalf(%) ;

Mathematica

First[RealDigits[PolyGamma[2, 1/3], 10, 100]] (* or *)
First[RealDigits[26*Zeta[3] + 4/9*Sqrt[3]*Pi^3, 10, 100]] (* Paolo Xausa, Nov 17 2025 *)

Prog

(PARI) -psi''(1/3) \\ Michel Marcus, Oct 23 2025

Crossrefs

Cf. A047787 (psi(1/3)), A390072 (psi'(1/3)).

Sequence in context: A174119 A156696 A232651 * A145227 A236555 A282969

Adjacent sequences: A390070 A390071 A390072 * A390074 A390075 A390076

Keyword

cons,nonn

Author

R. J. Mathar, Oct 23 2025

Status

approved