A261976 Expansion of elliptic_K / elliptic_E in powers of q.

1, 8, 16, -32, -96, 368, 960, -3392, -8896, 31528, 82656, -292704, -767616, 2719024, 7130496, -25257408, -66235776, 234616720, 615265872, -2179359392, -5715218752, 20244124928, 53088812352, -188048196544, -493143336192, 1746784492472, 4580821023328, -16225925666624

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: T3^5 / (T4^4 * T3 + 4*q * d/dq T3) where T3 = theta_3(q) and T4 = theta_4(q).

Crossrefs

Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).

Cf. A261979 ((K/E)^(1/2)), A261980 ((K/E)^(1/4)).

Cf. A261975 (E/K), A261977 ((E/K)^(1/2)), A261978 ((E/K)^(1/4)).

Sequence in context: A206375 A146541 A363014 * A291124 A239280 A043111

Adjacent sequences: A261973 A261974 A261975 * A261977 A261978 A261979

Keyword

sign

Author

Joerg Arndt, Sep 07 2015

Status

approved