Help needed!!

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!

Easy Math Editor

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Comments

Did 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 $\in [Novice^{+},Intermediate^{-}]$ !

A Former Brilliant Member - 6 years, 3 months ago

:D Interesting interval there.

Soumo Mukherjee - 6 years, 3 months ago

Haha yes!

A Former Brilliant Member - 6 years, 3 months ago

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

Kartik Sharma - 6 years, 3 months ago

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

Kartik Sharma - 6 years, 3 months ago

and more! @Brilliantians! Please help!

Kartik Sharma - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$