Polynomial expansions for solution of wave equation in quantum calculus

Abstract

In this paper, using the q^2 -Laplace transform early introduced by Abdi [1], we study q-Wave polynomials related with the q-difference operator ∆q,x . We show in particular that they are linked to the q-little Jacobi polynomials p_n (x; α, β | q^2 ).

Keywords

• Quantum calculus
• Wave polynomial
• q-analysis
• q-integral transform