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

Author

Benoit Cloitre, May 24 2003

Keywords

• cons
• nonn

Comments

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

Examples

			3.1320337...
		

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
• Index entries for sequences related to the digamma function

Programs

Magma

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

Mathematica

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

PARI

Euler+(3/2)*log(3)+Pi/(2*sqrt(3))

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).