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 A243308 Decimal expansion of h_3, a constant related to certain evaluations of the gamma function from elliptic integrals. 1
 1, 0, 1, 7, 4, 0, 8, 7, 9, 7, 5, 9, 5, 9, 5, 6, 0, 0, 8, 6, 6, 9, 5, 3, 8, 7, 5, 3, 3, 5, 0, 0, 6, 3, 4, 2, 5, 9, 9, 5, 2, 5, 6, 9, 1, 8, 5, 4, 5, 4, 1, 1, 8, 9, 9, 9, 1, 5, 0, 5, 4, 2, 3, 7, 5, 3, 5, 2, 1, 2, 4, 3, 1, 8, 0, 6, 2, 5, 0, 1, 6, 3, 9, 4, 4, 2, 3, 6, 6, 6, 5, 0, 9, 7, 6, 1, 2, 0, 0, 7, 9, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5.4 Gamma function, p. 34. LINKS Table of n, a(n) for n=1..103. Eric Weisstein's MathWorld, Gamma function FORMULA 4*K(4*sqrt(3)-7)/(sqrt(2+sqrt(3))*Pi), where K is the complete elliptic integral of the first kind. 3^(1/4)*GAMMA(1/3)^3/(2*2^(1/3)*Pi^2), where GAMMA is the Euler Gamma function. GAMMA(1/6)^(3/2)/(2^(5/6)*sqrt(3)*Pi^(5/4)). EXAMPLE 1.0174087975959560086695387533500634259952569... MAPLE Re(evalf(4*EllipticK(sqrt((4*sqrt(3)-7)))/(sqrt(2+sqrt(3))*Pi), 120)); # Vaclav Kotesovec, Apr 22 2015 MATHEMATICA RealDigits[4*EllipticK[4*Sqrt[3]-7]/(Sqrt[2+Sqrt[3]]*Pi), 10, 103] // First RealDigits[1/ArithmeticGeometricMean[1, Sqrt[2 + Sqrt[3]]/2], 10, 103][[1]] (* Jan Mangaldan, Jan 06 2017 *) RealDigits[2 EllipticK[(2 - Sqrt[3])/4]/Pi, 10, 103][[1]] (* Jan Mangaldan, Jan 06 2017 *) CROSSREFS Cf. A073005, A175379, A175574. Sequence in context: A196624 A157413 A258500 * A293609 A294514 A099935 Adjacent sequences: A243305 A243306 A243307 * A243309 A243310 A243311 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jun 03 2014 STATUS approved

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Last modified May 30 12:57 EDT 2023. Contains 363050 sequences. (Running on oeis4.)