Sums of series of the form $\sum\limits^{\infty}_{k=1}\frac{1}{k^2+ak+b}$

The article considers the possibility of reducing the sum of a series of the indicated type to elementary functions — both directly and in terms of some approximations. For this it is convenient to use the symmetric meromorphic function of two variables $\sum\limits^{\infty}_{k=1}\frac{1}{k^2+ak+b}$.