On Computing Sums of Double Numerical Series

In this study, we obtain the sums of three families of double numerical series not mentioned in existing handbooks. These sums are expressed by means of known special functions, namely the Bessel function and the modified Bessel function. The technique is based on computing the resultant using two different methods. The first method uses the formula for the resultant of an entire function and a polynomial (or an entire function with a finite number of zeros) previously obtained by A. M. Kytmanov and E. K. Myshkina. The second method computes the resultant as the product of values of one function at the roots of another. The proposed approach for computing the sums of double numerical series differs significantly from methods based on residue integrals associated with a system of equations.