Re: Theta function integration bug
- To: mathgroup at smc.vnet.net
- Subject: [mg126866] Re: Theta function integration bug
- From: derivatorb at gmail.com
- Date: Thu, 14 Jun 2012 05:31:56 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jr9km3$3kp$1@smc.vnet.net>
El mi=E9rcoles, 13 de junio de 2012 10:57:39 UTC+2, Sebastian Meznaric escribiF3:> The bug can be found in the following analytic integral:
> Integrate[
> EllipticTheta[3, \[Phi], \[Alpha]] Exp[I \[Phi]], {\[Phi], 0,
> 2 \[Pi]}]
>
> Mathematica evaluates the integral to 0, which is not correct, which can be seen considering that for small value of alpha, the elliptic theta is close to the delta function. Numerical integration also confirms that this integral is non-zero.
>From the definition
1 + 2 Sum[\[Alpha]^(n^2) Cos[2 n \[Phi]], {n, 1, Infinity}],
it is clear that
EllipticTheta[3, \[Phi], \[Alpha]]
contains only Fourier modes
E^(I k \[Phi]
with even k. So the integral you propose is actually zero.
When \[Alpha] is zero EllipticTheta[3, \[Phi], \[Alpha]] is equal to constant unity.