A089799 Expansion of Jacobi theta function theta_2(q^(1/2))/q^(1/8).

2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

I. J. Zucker, Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums, J. Phys. A: Math. Gen. 23, 117-132, 1990.

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = exp(Pi / 8) * Pi^(1/4) * 2^(3/8) / Gamma(3/4) = A388474. - Simon Plouffe, Sep 17 2025

Mathematica

a[n_] := SeriesCoefficient[ EllipticTheta[2, 0, q^(1/2)]/q^(1/8), {q, 0, n}]; Table[a[n], {n, 0, 101}] (* Jean-François Alcover, Nov 12 2012 *)

Crossrefs

Sequence in context: A273127 A103272 A065710 * A073464 A142242 A362634

Adjacent sequences: A089796 A089797 A089798 * A089800 A089801 A089802

Keyword

nonn

Author

Eric W. Weisstein, Nov 12 2003

Status

approved