Remarkable properties of the sincp,q functions and related integrals

Houry Melkonian; Shingo Takeuchi

doi:10.1016/j.jmaa.2021.124981

Remarkable properties of the sinc_p,q functions and related integrals

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

Abstract

Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised sin_p,q in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising but interesting generalisation of the identity between the Dirichlet integral and that of the integrand sinc² is discovered. Moreover, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.

Original language	English
Article number	124981
Journal	Journal of Mathematical Analysis and Applications
Volume	499
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.124981
Publication status	Published - 2021 Jul 1

Keywords

Asymptotic expansion
Ball's integral inequality
Dirichlet integral
Generalised trigonometric functions
p-Laplace operator

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2021.124981

Cite this

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title = "Remarkable properties of the sincp,q functions and related integrals",

abstract = "Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised sinp,q in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising but interesting generalisation of the identity between the Dirichlet integral and that of the integrand sinc2 is discovered. Moreover, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.",

keywords = "Asymptotic expansion, Ball's integral inequality, Dirichlet integral, Generalised trigonometric functions, p-Laplace operator",

author = "Houry Melkonian and Shingo Takeuchi",

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AU - Takeuchi, Shingo

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