OFFSET
1,1
REFERENCES
Richard E. Crandall, Projects in Scientific Computation, Springer, 1994; see p. 48.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
Equals (2*((6 + sqrt(3) + 4*sqrt(2 + sqrt(3)))*E((-2 + sqrt(2 + sqrt(3)))^2/(2 + sqrt(2 + sqrt(3)))^2) - 4*sqrt(2 + sqrt(3))*K((-2 + sqrt(2 + sqrt(3)))^2/ (2 + sqrt(2 + sqrt(3)))^2)))/(2 + sqrt(2 + sqrt(3))), where K and E are the elliptic integrals of first and second kind.
Equals sqrt(Pi/sqrt(3))*(((1 + 1/sqrt(3))*Gamma(1/3))/Gamma(5/6) + (2*Gamma(5/6))/Gamma(1/3)).
EXAMPLE
6.176601987658693464745684084107374417575372343469612510291144192254...
MATHEMATICA
p = Sqrt[Pi/Sqrt[3]]*((1 + 1/Sqrt[3])*Gamma[1/3]/Gamma[5/6] + 2*Gamma[5/6]/ Gamma[1/3]);
RealDigits[p, 10, 103][[1]]
PROG
(PARI) sqrt(Pi/sqrt(3))*((1 + 1/sqrt(3))*gamma(1/3)/gamma(5/6) + 2*gamma(5/6)/gamma(1/3)) \\ _G. C. Greubel, Jun 05 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 10 2016
STATUS
approved