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A047787
Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function.
13
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
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...
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
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, May 24 2003
STATUS
approved