Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2012

[Date Index] [Thread Index] [Author Index]

Search the Archive

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.



  • Prev by Date: Re: Strongly connected graph in mathematica 8?
  • Next by Date: Re: FrameLabel and Style
  • Previous by thread: Theta function integration bug
  • Next by thread: Re: Theta function integration bug