I am interested in knowing how to calculate infinite products like (or reading any reference about it):

$$\prod_{j=1}^{\infty}\left( 1-\left( \frac{x}{a+j\pi} \right) ^2 \right)$$

Inserting it into a Mathematica worksheet (Wolfram research), it returns the following beautiful formula:

$$\frac{\pi^2\Gamma(\frac{\pi+a}{\pi})^2}{\Gamma(\frac{a-x}{\pi})\Gamma(\frac{a+x}{\pi})}$$

where $\Gamma(x)$ is the Euler's Gamma function, and $x$ and $a$ are positive real numbers.

Thanks in advance,

Gustavo