Work

On Computing Sums of Double Numerical Series

Year: 2026

Type: article

Abstract: 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.

Source: Mathematics

DOI: 10.3390/math14183296

Authors: Vyacheslav I. Kuzovatov, Alexey A. Kytmanov, Evgeniya K. Myshkina

Institutions: Siberian Federal University, MIREA - Russian Technological University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Russian Science Foundation