A274346 Denominators of coefficients in the expansion of (log(q) - log(k^2/16))/(8*k^2/16) in powers of k^2/16, where q is the Jacobi nome and k^2 the parameter of elliptic functions.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 15, 16, 17, 9, 19, 5, 21, 11, 23, 3, 25, 1, 27, 7, 29, 3, 31, 32, 33, 17, 35, 9, 37, 19, 39, 5, 41, 21, 43, 11, 9, 23, 47, 6, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 64, 1, 33, 67, 17, 3, 35, 71, 9, 73, 37, 75, 19, 11, 39, 79, 10

Offset: 0

Author

Wolfdieter Lang, Jun 30 2016

Keywords

• nonn
• easy
• frac

Comments

The numerators are given in A274345, where also details and the first rationals are given.

The Mathematica program below gives the rationals r(n-1), n = 1..50.

Crossrefs

Cf. A227503, A274345.

Programs

Mathematica

Table[SeriesCoefficient[Log[EllipticNomeQ[16 x]/x]/8, {x, 0, n}], {n, 1, 50}] // Denominator (* Vaclav Kotesovec, Jun 30 2016 *)

Formula

a(n) = denominator(A227503(n+1)/(n+1)), n >= 0.

(log(q) - log(k^2/16))/(8*k^2/16) = Sum_{n >= 0} (A274345(n)/a(n))*(k^2/16)^n.

Extensions

More terms from Vaclav Kotesovec, Jun 30 2016