Investigating the Properties and Dynamic Applications of Δ h Legendre–Appell Polynomials

Noor Alam, Shahid Ahmad Wani (), Waseem Ahmad Khan and Hasan Nihal Zaidi
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Noor Alam: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Shahid Ahmad Wani: Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, Maharashtra, India
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Hasan Nihal Zaidi: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2024, vol. 12, issue 13, 1-14

Abstract: This research aims to introduce and examine a new type of polynomial called the Δ h Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δ h Legendre–Appell polynomials and explore their properties. We derive the generating function and recurrence relations for these polynomials and their explicit formulas, recurrence relations, and summation formulas. We also verify the monomiality principle for these polynomials and express them in determinant form. Additionally, we establish similar results for the Δ h Legendre–Bernoulli, Euler, and Genocchi polynomials.

Keywords: ? h sequences; monomiality principle; Legendre–Appell polynomials; explicit forms; determinant form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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