A047787 Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function.

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

Offset

1,1

Comments

Decimal expansion of -psi(1/3). - Benoit Cloitre, Mar 07 2004

References

S. J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

E. D. Krupnikov, K. S. Kolbig,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

Gamma'(1/3)/Gamma(1/3)=-EulerGamma-(3/2)*log(3)-Pi/(2*sqrt(3))=-3.13203378002... where EulerGamma is the Euler-Mascheroni constant (A001620).

Example

3.1320337...

Maple

-Psi(1/3) ; evalf(%) ; # R. J. Mathar, Oct 23 2025

Mathematica

RealDigits[PolyGamma[1/3], 10, 105] // First (* Jean-François Alcover, Aug 08 2015 *)

Prog

(PARI) Euler+(3/2)*log(3)+Pi/(2*sqrt(3))
(Magma) SetDefaultRealField(RealField(100)); R:= RealField();
EulerGamma(R) + (3/2)*Log(3) + Pi(R)/(2*Sqrt(3)); // G. C. Greubel, Aug 28 2018

Crossrefs

Sequence in context: A262026 A270390 A341472 * A102668 A243848 A271617

Adjacent sequences: A047784 A047785 A047786 * A047788 A047789 A047790

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2003

Status

approved