Remarkable properties of the sincp,q functions and related integrals

Houry Melkonian, Shingo Takeuchi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number124981
JournalJournal of Mathematical Analysis and Applications
Volume499
Issue number1
DOIs
Publication statusPublished - 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

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