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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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 \(\in [Novice^{+},Intermediate^{-}]\) ! – Azhaghu Roopesh M · 2 years, 2 months ago

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– Soumo Mukherjee · 2 years, 2 months ago

:D Interesting interval there.Log in to reply

– Azhaghu Roopesh M · 2 years, 2 months ago

Haha yes!Log in to reply

– Kartik Sharma · 2 years, 2 months ago

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

@Ronak Agarwal @Pratik Shastri @Azhaghu Roopesh M @Jon Haussmann @Brian Charlesworth – Kartik Sharma · 2 years, 2 months ago

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– Kartik Sharma · 2 years, 2 months ago

and more! @Brilliantians! Please help!Log in to reply