Summing Sneddon–Bessel series explicitly

Durán, Antonio J. ; Pérez, Mario (Universidad de Zaragoza) ; Varona, Juan Luis

Resumen: We sum in a closed form the Sneddon–Bessel series [fórmula] where 0 < X, 0 < y, x + y < 2, n is an integer, [fórmula] with [fórmula] and [fórmula] are the zeros of the Bessel function [fórmula] of order [fórmula]. In most cases, the explicit expressions for these sums involve hypergeometric functions [fórmula]. As an application, we prove some extensions of the Kneser–Sommerfeld expansion. For instance, we show that [fórmula] if Re v < Re B + 1 and [fórmula](here, Yv denotes the Bessel function of the second kind), which becomes the Kneser–Sommerfeld expansion when B = v.

Idioma: Inglés

DOI: 10.1002/mma.9939

Año: 2024

Publicado en: Mathematical Methods in the Applied Sciences 47, 7 (2024), 6590-6606
ISSN: 0170-4214

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-124332NB-C21
Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-124332NB-C22
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)