Startseite The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials
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The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials

  • Saddam Husain ORCID logo , Nabiullah Khan , Talha Usman ORCID logo EMAIL logo und Junesang Choi
Veröffentlicht/Copyright: 30. November 2023
Analysis
Aus der Zeitschrift Analysis Band 44 Heft 1

Abstract

The introduction of two-parameter ( p , q ) -calculus and Lie algebras in 1991 has spurred a wave of recent research into ( p , q ) -special polynomials, including ( p , q ) -Bernoulli, ( p , q ) -Euler, ( p , q ) -Genocchi and ( p , q ) -Frobenius–Euler polynomials. These investigations have been carried out by numerous researchers in order to uncover a wide range of identities associated with these polynomials and applications. In this article, we aim to introduce ( p , q ) -sine and ( p , q ) -cosine based λ-array type polynomials and derive numerous properties of these polynomials such as ( p , q ) -integral representations, ( p , q ) -partial derivative formulae and ( p , q ) -addition formulae. It is worth noting that the utilization of the ( p , q ) -polynomials introduced in this study, along with other ( p , q ) -polynomials, can lead to the derivation of various identities that differ from the ones presented here.

Funding statement: The third author Talha Usman would like to thank Scientific Research Department at University of Technology and Applied Sciences, Sur for supporting this work under Project No. UTAS-Sur-SRD-IRF 23-04/06.

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Received: 2023-05-12
Revised: 2023-08-21
Accepted: 2023-09-03
Published Online: 2023-11-30
Published in Print: 2024-02-01

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