Abstract.

In this article, the operational definitions and integral representations are combined to introduce new families of the generalized Legendre and generalized Legendre-Appell polynomials. The explicit summation formulae, determinant definitions and recurrence relations for the generalized Legendre-Appell polynomials are derived by making use of the integral transforms and appropriate operational rules. An analogous study of these results for the generalized Legendre-Bernoulli, Legendre-Euler and Legendre-Genocchi polynomials is presented. Several identities for these polynomials are also derived by employing appropriate operational definitions.

Keywords:

Appell polynomials, Legendre polynomials, Legendre-Appell polynomials; fractional operators, operational rules, determinant definition.