圆周率的一种无穷级数

\[ \left( \frac{1}{2}+\sum_{n=1}^{\infty}{\frac{1}{4n^2+1}} \right) \left( \frac{1}{2}+\sum_{n=1}^{\infty}{\frac{1}{4n^4+1}} \right) =\frac{\pi ^2}{16} \]