MathGroup Archive 2005

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Infinite sum of gaussians

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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