# 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:

This is a part of the set Formidable Series and Integrals

Note by Hummus A
2 years, 2 months ago

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

- 2 years, 2 months ago