New Identities Involving the Univariate Lommel and Bessel Functions

Carlos M. da Fonseca∗; M. Lawrence Glasser; Victor Kowalenko

doi:10.2298/AADM240809015F

New Identities Involving the Univariate Lommel and Bessel Functions

Carlos M. da Fonseca∗
, M. Lawrence Glasser
, Victor Kowalenko

Kuwait College of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We extend our previous work on integral representations of the univariate Lommel function, originally linked to Chebyshev polynomials of the first kind. This study presents new identities involving other special functions, such as Bessel functions, and introduces connections with Chebyshev polynomials of the second kind. Additional integral representations are also derived using elementary functions.

Original language	English
Pages (from-to)	348-369
Number of pages	22
Journal	Applicable Analysis and Discrete Mathematics
Volume	19
Issue number	2
DOIs	https://doi.org/10.2298/AADM240809015F
State	Published - Jan 2025

Keywords

Bessel function
Carlson's theorem
Chebyshev polynomials
integral
limit identity
univariate Lommel function

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10.2298/AADM240809015F

Cite this

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title = "New Identities Involving the Univariate Lommel and Bessel Functions",

abstract = "We extend our previous work on integral representations of the univariate Lommel function, originally linked to Chebyshev polynomials of the first kind. This study presents new identities involving other special functions, such as Bessel functions, and introduces connections with Chebyshev polynomials of the second kind. Additional integral representations are also derived using elementary functions.",

keywords = "Bessel function, Carlson's theorem, Chebyshev polynomials, integral, limit identity, univariate Lommel function",

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AU - Kowalenko, Victor

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AB - We extend our previous work on integral representations of the univariate Lommel function, originally linked to Chebyshev polynomials of the first kind. This study presents new identities involving other special functions, such as Bessel functions, and introduces connections with Chebyshev polynomials of the second kind. Additional integral representations are also derived using elementary functions.

KW - Bessel function

KW - Carlson's theorem

KW - Chebyshev polynomials

KW - integral

KW - limit identity

KW - univariate Lommel function

UR - https://www.scopus.com/pages/publications/105028694907

U2 - 10.2298/AADM240809015F

DO - 10.2298/AADM240809015F

M3 - Article

AN - SCOPUS:105028694907

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EP - 369

JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 2

ER -

New Identities Involving the Univariate Lommel and Bessel Functions

Abstract

Keywords

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