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Infinite sum of gaussians

• To: mathgroup at smc.vnet.net
• Subject: [mg55955] Infinite sum of gaussians
• From: "Valeri Astanoff" <astanoff at yahoo.fr>
• Date: Tue, 12 Apr 2005 05:26:04 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Dear group,

Could anyone prove or disprove this equality, at least for z being real
:

Sum[Exp[-((z - k)^2/2)], {k, -Infinity, Infinity}] ==
 Sqrt[2*Pi] + Cos[2*Pi*z]*(EllipticTheta[3, 0, 1/Sqrt[E]] - Sqrt[2*Pi])

?


Valeri

• Follow-Ups:
  • Re: Infinite sum of gaussians
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>