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Theta function integration bug

• To: mathgroup at smc.vnet.net
• Subject: [mg126849] Theta function integration bug
• From: Sebastian Meznaric <meznaric at gmail.com>
• Date: Wed, 13 Jun 2012 04:55:55 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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.