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Re: Theta function integration bug

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126864] Re: Theta function integration bug
  • From: Robert Miller <robertelmiller at gmail.com>
  • Date: Thu, 14 Jun 2012 05:31:15 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jr9km3$3kp$1@smc.vnet.net>

Look at the series expansion of EllipticTheta[3,\[Phi], \[Alpha]] in the Documentation Center or find it on the web.

EllipticTheta[3, \[Phi], \[Alpha]]=1 + 2*Sum[\[Alpha]^n^2*Cos[2*n*\[Phi]], {n, 1, Infinity}]

Clear from this that if you multiply by E^I\[Phi]and perform your integral, every term in the series is equal to zero. I don't think there is a bug.

Robert
On Wednesday, June 13, 2012 1:57:39 AM UTC-7, Sebastian Meznaric wrote:
> 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.



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