I was just reading Feynman lectures and there was a series which came there. There its value was assumed. But I thought it must be having a value as it is converging. But it was really difficult to find a closed form. The series was -

\[\displaystyle \sum_{k=0}^{\infty}{\frac{{(-1)}^{k}}{\sqrt{{x}^{2}+{k}^{2}}}}\]

I learnt Fourier Transform and Poisson sum formula too but they are not helping me. Actually the topic was electrostatic energy of an ionic crystal.

Any type of help will be appreciated!

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## Comments

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TopNewestDid you look up Ewald's summation ? As far as I know , fourier transform comes up in that summation only , and if that is indeed the case , sorry because I \(\in [Novice^{+},Intermediate^{-}]\) !

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:D Interesting interval there.

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Haha yes!

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Well, it came in one of Pratik's questions as well and that question is quite a bit same as this one.

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@Ronak Agarwal @Pratik Shastri @Azhaghu Roopesh M @Jon Haussmann @Brian Charlesworth

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and more! @Brilliantians! Please help!

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