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.

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

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 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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