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arXiv · 2005.00477

Remarkable properties of the $\text{sinc}_{p, q}$ functions and related integrals

Houry Melkonian·Shingo Takeuchi
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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 $\text{sinc}^2$ is discovered. Moreover, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.

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Houry Melkonian, Shingo Takeuchi. 2020-05-01. Remarkable properties of the $\text{sinc}_{p, q}$ functions and related integrals. https://doi.org/10.1016/j.jmaa.2021.124981

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