# Wait. Number Theory?

Calculus Level 5

$\large\sum _{n=1}^{\infty}\sum _{m=1}^{\infty}\dfrac{1}{(m^2+n^2)^2}=\dfrac{\pi^a}{b}G - \dfrac{\pi^d}{f}$

The equation above holds true for positive integers $$a,b,d$$ and $$f$$. Find $$a+b+d+f$$.

 Notation: $$\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916$$ denotes the Catalan's constant.

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