Remarkable properties of the sincp,q functions and related integrals

Houry Melkonian; Shingo Takeuchi

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.

MSC Codes Primary 33B10, 33F99, Secondary 42A99

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 May 1

Keywords

Asymptotic expansion
Ball’s integral inequality
Dirichlet integral
Generalised trigonometric functions
P-Laplace operator

ASJC Scopus subject areas

General

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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{\textquoteright}s integral inequality is obtained in terms of two parameters.MSC Codes Primary 33B10, 33F99, Secondary 42A99",

keywords = "Asymptotic expansion, Ball{\textquoteright}s integral inequality, Dirichlet integral, Generalised trigonometric functions, P-Laplace operator",

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AU - Melkonian, Houry

AU - Takeuchi, Shingo

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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.MSC Codes Primary 33B10, 33F99, Secondary 42A99

AB - 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.MSC Codes Primary 33B10, 33F99, Secondary 42A99

KW - Asymptotic expansion

KW - Ball’s integral inequality

KW - Dirichlet integral

KW - Generalised trigonometric functions

KW - P-Laplace operator

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