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 A274014 Decimal expansion of the arc length of an ellipse with semi-major axis 1 and eccentricity sin(Pi/12), an arc length which evaluates without using elliptic integrals (a computation due to Ramanujan). 2
 6, 1, 7, 6, 6, 0, 1, 9, 8, 7, 6, 5, 8, 6, 9, 3, 4, 6, 4, 7, 4, 5, 6, 8, 4, 0, 8, 4, 1, 0, 7, 3, 7, 4, 4, 1, 7, 5, 7, 5, 3, 7, 2, 3, 4, 3, 4, 6, 9, 6, 1, 2, 5, 1, 0, 2, 9, 1, 1, 4, 4, 1, 9, 2, 2, 5, 4, 1, 1, 3, 1, 0, 3, 2, 7, 8, 6, 3, 0, 1, 9, 0, 0, 3, 0, 5, 9, 1, 8, 7, 3, 8, 6, 0, 1, 5, 4, 3, 2, 9, 3, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
 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 Cf. A019824. Sequence in context: A330062 A198420 A110942 * A334962 A082830 A261622 Adjacent sequences: A274011 A274012 A274013 * A274015 A274016 A274017 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Jun 10 2016 STATUS approved

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Last modified August 12 13:41 EDT 2024. Contains 375113 sequences. (Running on oeis4.)