Prove that:-
[tex] \rm \sum_{n = 1}^ \infty \frac{1}{ {n}^{2} + {x}^{2} } = \frac{\pi x - 1 }{2 {x}^{2} } + \frac{\pi}{x( {e}^{2 \pi x} - 1)} \\ [/tex]

Question

30-09-2022
Mathematics

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Prove that:-
[tex] \rm \sum_{n = 1}^ \infty \frac{1}{ {n}^{2} + {x}^{2} } = \frac{\pi x - 1 }{2 {x}^{2} } + \frac{\pi}{x( {e}^{2 \pi x} - 1)} \\ [/tex]

Sagot :

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Prove that:-[tex] \rm \sum_{n = 1}^ \infty \frac{1}{ {n}^{2} + {x}^{2} } = \frac{\pi x - 1 }{2 {x}^{2} } + \frac{\pi}{x( {e}^{2 \pi x} - 1)} \\ [/tex]​

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Prove that:-
[tex] \rm \sum_{n = 1}^ \infty \frac{1}{ {n}^{2} + {x}^{2} } = \frac{\pi x - 1 }{2 {x}^{2} } + \frac{\pi}{x( {e}^{2 \pi x} - 1)} \\ [/tex]