Differential and integral equations for Legendre-Laguerre based hybrid polynomials

Abstract

UDC 517.9 In this article, a hybrid family of three-variable Legendre – Laguerre – Appell polynomials is explored and their properties including the series expansions, determinant forms, recurrence relations, shift operators, followed by differential, integro-differential and partial differential equations are established. The analogous results for the three-variable Hermite – Laguerre – Appell polynomials are deduced. Certain examples in terms of Legendre – Laguerre – Bernoulli, –E uler and – Genocchi polynomials are constructed to show the applications of main results. A further investigation is performed by deriving homogeneous Volterra integral equations for these polynomials and for their relatives.