Work

New Results for Certain Jacobsthal-Type Polynomials

Year: 2025

Type: article

Abstract: This paper investigates a class of Jacobsthal-type polynomials (JTPs) that involves one parameter. We present several new formulas for these polynomials, including expressions for their derivatives, moments, and linearization formulas. The key idea behind the derivation of these formulas is based on developing a new connection formula that expresses the shifted Chebyshev polynomials of the third kind in terms of the JTPs. This connection formula is used to deduce a new inversion formula of the JTPs. Therefore, by utilizing the power form representation of these polynomials and their corresponding inversion formula, we can derive additional expressions for them. Additionally, we compute some definite integrals based on some formulas of these polynomials.

Source: Mathematics

DOI: 10.3390/math13050715

Authors: Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Amr Kamel Amin

Institutions: Cairo University, University of Jeddah, Beni-Suef University, Umm al-Qura University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Umm Al-Qura University