A089798 Expansion of Jacobi theta function theta_4(q^2).

1, 0, -2, 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, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0

Offset: 0

Author

Eric W. Weisstein, Nov 12 2003

Keywords

• sign

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.

Crossrefs

Cf. A002448.

Programs

Mathematica

a[n_] := SeriesCoefficient[ EllipticTheta[4, 0, q^2], {q, 0, n}]; Table[a[n], {n, 0, 101}] (* Jean-François Alcover, Nov 12 2012 *)

PARI

for(n=0,50, print1(if(n==0, 1, 2*(floor(sqrt(n/2)) - floor(sqrt((n-1)/2)))*(-1)^floor(sqrt(n/2))), ", ")) \\ G. C. Greubel, Nov 20 2017

Formula

For n > 0, a(n) = 2*(floor(sqrt(n/2)) - floor(sqrt((n-1)/2)))*(-1)^floor(sqrt(n/2)). - Mikael Aaltonen, Jan 18 2015