TY - JOUR
T1 - Remarkable properties of the sincp,q functions and related integrals
AU - Melkonian, Houry
AU - Takeuchi, Shingo
N1 - Funding Information:
We thank the referees for their careful reading of our manuscript and for their insightful comments. The work of ST was supported by JSPS KAKENHI Grant Number 17K05336 . HM thanks Prof. D.E. Edmunds for his invaluable and generous comments, and endorses her former MSc student Mr. Andrew Pritchard for obtaining (independent of this work) an argument analogous to that of Corollary 2.1 .
Publisher Copyright:
© 2021 The Authors
PY - 2021/7/1
Y1 - 2021/7/1
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.
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.
KW - Asymptotic expansion
KW - Ball's integral inequality
KW - Dirichlet integral
KW - Generalised trigonometric functions
KW - p-Laplace operator
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U2 - 10.1016/j.jmaa.2021.124981
DO - 10.1016/j.jmaa.2021.124981
M3 - Article
AN - SCOPUS:85100223517
SN - 0022-247X
VL - 499
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 124981
ER -