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A257437 Decimal expansion of G(1/12), a generalized Catalan constant. 4
9, 1, 2, 0, 5, 5, 0, 8, 9, 3, 7, 2, 7, 1, 8, 4, 0, 0, 0, 1, 8, 8, 2, 8, 6, 5, 5, 6, 9, 3, 0, 9, 7, 5, 3, 4, 4, 5, 1, 1, 4, 2, 9, 1, 1, 9, 8, 0, 3, 1, 8, 7, 4, 6, 8, 4, 3, 6, 2, 4, 2, 6, 1, 7, 8, 4, 7, 8, 3, 6, 9, 1, 3, 8, 3, 6, 5, 2, 7, 4, 1, 1, 1, 5, 0, 3, 4, 6, 4, 5, 0, 4, 7, 5, 7, 7, 3, 5, 5, 7, 2, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

D. Borwein, J. M. Borwein, M. L. Glasser, J. G Wan, Moments of Ramanujan's Generalized Elliptic Integrals and Extensions of Catalan's Constant, 2010.

D. Borwein, J. M. Borwein, M. L. Glasser, J. G Wan, Moments of Ramanujan's Generalized Elliptic Integrals and Extensions of Catalan's Constant, Journal of Mathematical Analysis and Applications, Volume 384, Issue 2, 15 December 2011, Pages 478-496.

FORMULA

G(s) = (Pi/4) * 3F2(1/2, 1/2-s, s+1/2; 1, 3/2; 1), with 2F1 the hypergeometric function.

G(s) = (1/(8*s))*(Pi + cos(Pi*s)*(psi(1/4+s/2) - psi(3/4+s/2))), where psi is the digamma function (PolyGamma).

G(1/12) = 3*(sqrt(3)+1)*(log(sqrt(2)-1) + (sqrt(3)/2)*log(sqrt(3)+sqrt(2))).

EXAMPLE

0.91205508937271840001882865569309753445114291198031874684362426...

MATHEMATICA

RealDigits[3*(Sqrt[3]+1)*(Log[Sqrt[2]-1] + (Sqrt[3]/2)*Log[Sqrt[3]+ Sqrt[2]]), 10, 103] // First

N[Pi*HypergeometricPFQ[{5/12, 1/2, 7/12}, {1, 3/2}, 1]/4, 106] (* Vaclav Kotesovec, Apr 24 2015 *)

PROG

(PARI) 3*(sqrt(3)+1)*(log(sqrt(2)-1) + (sqrt(3)/2)*log(sqrt(3)+ sqrt(2))) \\ G. C. Greubel, Aug 24 2018

(MAGMA) SetDefaultRealField(RealField(100)); 3*(Sqrt(3)+1)*(Log(Sqrt(2)-1) + (Sqrt(3)/2)*Log(Sqrt(3)+ Sqrt(2))) // G. C. Greubel, Aug 24 2018

CROSSREFS

Cf. A006752 (G(0) = Catalan), A257435 (G(1/6)), A091648 (G(1/4)), A257436 (G(1/3)), A257438 (G(1/5)).

Sequence in context: A176647 A068452 A021527 * A339757 A010166 A186116

Adjacent sequences:  A257434 A257435 A257436 * A257438 A257439 A257440

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Apr 23 2015

STATUS

approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)