So many cool constants!

$\Large \prod _{ n=0 }^{ \infty }{ \frac { \left( 4n+3 \right) ^{ \frac { 1 }{ 4n+3 } } }{ \left( 4n+1 \right) ^{ \frac { 1 }{ 4n+1 } } } } =\frac { { 2 }^{ \pi /2 }{ e }^{ \gamma \pi /4 }{ \pi }^{ 3\pi /4 } }{ \Gamma ^{ \pi }(1/4) }$

Prove the product above

Notations:

$\gamma$ denotes the Euler-Mascheroni constant, $\gamma \approx 0.5772$ .
$\Gamma(\cdot)$ denotes the Gamma function.

This is a part of the set Formidable Series and Integrals

#Calculus

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Comments

The proof is quite straightforward if you know the first proposition in this paper, just take the log of the product.

Haroun Meghaichi - 4 years, 12 months ago

Could you please check the link again??? It does not seem to work............@Hummus a Or, could you please guide me to the paper.......Thanks.......!!

Aaghaz Mahajan - 2 years, 5 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}`	$\boxed{123}$