It isn't an ordinary one!

Calculus Level 5

\[\large \sum _{ n=-\infty }^{ \infty }{ { e }^{ -{ \pi n }^{ 2 } } } =\dfrac { { \pi }^{A / B } }{ \Gamma \left( \frac { C }{ D } \right) } \]

The equation above holds true for positive integers \(A,B,C\) and \(D\) with \(\gcd(A,B) = \gcd(C,D) = 1\). Find \(A+B+C+D\).

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