Work

Lommel functions, Padé approximants and hypergeometric functions

Year: 2024

Type: article

Abstract: We consider the Lommel functions s μ , ν ( z ) for different values of the parameters ( μ , ν ) . We show that if ( μ , ν ) are half integers, then it is possible to describe these functions with an explicit combination of polynomials and trigonometric functions. The polynomials turn out to give Padé approximants for the trigonometric functions. Numerical properties of the zeros of the polynomials are discussed. Also, when μ is an integer, s μ , ν ( z ) can be written as an integral involving an explicit combination of trigonometric functions. A closed formula for F 1 2 ( 1 2 + ν , 1 2 − ν ; μ + 1 2 ; sin ⁡ ( θ 2 ) 2 ) with μ an integer is given.

Source: Applied Numerical Mathematics

DOI: 10.1016/j.apnum.2024.11.003

Author: Federico Zullo

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca, University of Brescia

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,560

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Brescia, Gruppo Nazionale per la Fisica Matematica