login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089805 Expansion of Jacobi theta function (theta_4(q^6) - theta_4(q^(2/3)))/2/q^(2/3). 1

%I

%S 1,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,

%T 0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U -1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Expansion of Jacobi theta function (theta_4(q^6) - theta_4(q^(2/3)))/2/q^(2/3).

%H G. C. Greubel, <a href="/A089805/b089805.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%H I. J. Zucker, <a href="https://doi.org/10.1088/0305-4470/23/2/009">Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums</a>, J. Phys. A: Math. Gen. 23, 117-132, 1990.

%F a(2*n) = A089801(n). a(2*n + 1) = 0. - _Michael Somos_, Jun 30 2015

%t A089805[n_] := SeriesCoefficient[(EllipticTheta[4, 0, q^6] - EllipticTheta[4, 0, q^(2/3)])/(2*q^(2/3)), {q, 0, n}]; Table[A089805[n], {n, 0, 50}] (* _G. C. Greubel_, Nov 20 2017 *)

%Y Cf. A089801.

%K sign

%O 0,1

%A _Eric W. Weisstein_, Nov 12 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 04:26 EDT 2020. Contains 335538 sequences. (Running on oeis4.)