A020777 - OEIS

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A020777

Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where Gamma(x) denotes the Gamma function.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

S.J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135, 1995.

LINKS

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

E. D. Krupnikov, K. S. Kölbig, Some special cases of the generalized hypergeometric function (q+1)Fq, J. Comp. Appl. Math. 78 (1997) 79-95, psi(1/4).

Wikipedia, Digamma function

Index entries for sequences related to the digamma function

FORMULA

Gamma'(1/4)/Gamma(1/4) = -EulerGamma - 3*log(2) - Pi/2 where EulerGamma is the Euler-Mascheroni constant (A001620).

Pi = gamma(0,1/4) - gamma(0,3/4) = A020777 - A200134, where gamma(n,x) denotes the generalized Stieltjes constants. - Peter Luschny, May 16 2018

EXAMPLE

4.2274535333762654080895301460966835773672444387082422716552795595189567958...

MAPLE

evalf(gamma+3*log(2)+Pi/2) ; # R. J. Mathar, Nov 13 2011

evalf(abs(Psi(1/4))) ; # R. J. Mathar, Nov 19 2024

MATHEMATICA

EulerGamma + Pi/2 + Log[8] // RealDigits[#, 10, 105][[1]] & (* Jean-François Alcover, Jun 18 2013 *)

N[StieltjesGamma[0, 1/4], 99] (* Peter Luschny, May 16 2018 *)

PROG

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

(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R) + Pi(R)/2 + Log(8); // G. C. Greubel, Aug 28 2018

CROSSREFS

Cf. A001620, A200134, A301816.

Sequence in context: A261557 A270809 A087507 * A153810 A098134 A079191

Adjacent sequences: A020774 A020775 A020776 * A020778 A020779 A020780

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, May 24 2003

STATUS

approved