# Roots of Digamma

Calculus Level 5

$\large \sum _{ a\in \Psi }^{ }{ \frac { 1 }{ { a }^{ 3 } } } =-A\zeta \left( B \right) -{ \gamma }^{ C }-\frac { { \gamma \pi }^{ D } }{ E }$

The above equation, where $$\Psi$$ denotes all the roots of digamma function, holds true for positive integers $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ with $$B$$ being an odd integer. Find $$A+B+C+D+E$$.

Notation: $$\gamma$$ denotes the Euler-Mascheroni constant, $$\gamma \approx 0.5772$$.

×