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Infinite sum of gaussians

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

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])



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