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

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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

Log in to reply