A328127 G.f.: E(4*sqrt(x)) / K(4*sqrt(x)), where E(), K() are complete elliptic integrals.

1, -8, -16, -128, -1312, -15104, -186112, -2398208, -31898176, -434421248, -6025687552, -84808699904, -1207939190272, -17375932633088, -252046328713216, -3682284573851648, -54130292542567552, -800036763837307904, -11880834659028677632, -177181827571092267008

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..825

Vaclav Kotesovec, Graph - the asymptotic ratio (30000 terms)

Eric Weisstein's MathWorld, Complete Elliptic Integral of the First Kind.

Eric Weisstein's MathWorld, Complete Elliptic Integral of the Second Kind.

Formula

a(n) ~ -2^(4*n+1) / (n * log(n)^2) * (1 - (2*gamma + 8*log(2)) / log(n) + (3*gamma^2 + 24*log(2)*gamma + 48*log(2)^2 - Pi^2/2) / log(n)^2 + (-4*gamma^3 + 2*gamma*Pi^2 - 48*gamma^2*log(2) + 8*Pi^2*log(2) - 192*gamma*log(2)^2 - 256*log(2)^3 - 8*Zeta(3)) / log(n)^3 + (5*gamma^4 - 5*gamma^2*Pi^2 + Pi^4/12 + 80*gamma^3*log(2) - 40*gamma*Pi^2*log(2) + 480*gamma^2*log(2)^2 - 80*Pi^2*log(2)^2 + 1280*gamma*log(2)^3 + 1280*log(2)^4 + 40*gamma*Zeta(3) + 160*log(2)*Zeta(3)) / log(n)^4), where gamma is the Euler-Mascheroni constant A001620.

Maple

seq(coeff(series(EllipticE(4*sqrt(x))/EllipticK(4*sqrt(x)), x, 21), x, n), n = 0..20);

Mathematica

CoefficientList[Series[EllipticE[16*x]/EllipticK[16*x], {x, 0, 20}], x]

Crossrefs

Cf. A010370, A054474, A261975, A328128.

Sequence in context: A277364 A278312 A107906 * A323385 A061359 A330150

Adjacent sequences: A328124 A328125 A328126 * A328128 A328129 A328130

Keyword

sign

Author

Vaclav Kotesovec, Oct 04 2019

Status

approved