Prove it!

$\displaystyle\sum _{ n=1 }^{ \infty }{ \frac { \zeta (2n,x) }{ 4^{ n }(2n^{ 2 }+n) } } =(2x-1)\ln { (x-\frac { 1 }{ 2 }) } -2x+1+\ln { 2\pi } -2\ln { \Gamma (x) }$

Prove the equation above, where $\zeta(s,x)$ denotes the Hurwitz zeta function

#Calculus

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

-1/2 +1 what is that check your question... Again :/

Aman Rajput - 5 years, 3 months ago

the 1/2 is supposed to be inside the ln,sorry for the confusion :)

Hamza A - 5 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}`	$\boxed{123}$