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 A261975 Expansion of elliptic_E / elliptic_K in powers of q. 7
 1, -8, 48, -224, 864, -2928, 9024, -25792, 69312, -176936, 432288, -1016736, 2312832, -5107504, 10983552, -23060544, 47373696, -95401872, 188637936, -366744160, 701930304, -1324016896, 2463662016, -4526174784, 8216376576, -14747939768, 26191413024, -46048199360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: (T4^4 * T3 + 4*q * d/dq T3) / T3^5 where T3 = theta_3(q) and T4 = theta_4(q). MATHEMATICA nmax = 30; dtheta = D[Normal[Series[EllipticTheta[3, 0, x], {x, 0, nmax}]], x]; CoefficientList[Series[(EllipticTheta[4, 0, x]^4*EllipticTheta[3, 0, x] + 4*x*dtheta)/EllipticTheta[3, 0, x]^5, {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 10 2018 *) CROSSREFS Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2). Cf. A261975 (E/K), A261977 ((E/K)^(1/2)), A261978 ((E/K)^(1/4)). Cf. A261976 (K/E), A261979 ((K/E)^(1/2)), A261980 ((K/E)^(1/4)). Sequence in context: A128796 A093199 A263507 * A087914 A271061 A211012 Adjacent sequences: A261972 A261973 A261974 * A261976 A261977 A261978 KEYWORD sign AUTHOR Joerg Arndt, Sep 07 2015 STATUS approved

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Last modified September 19 02:20 EDT 2024. Contains 376003 sequences. (Running on oeis4.)