Study of generalized Legendre-Appell polynomials via fractional operators. (English) Zbl 1517.33002
Summary: 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.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 26A33 | Fractional derivatives and integrals |
| 33B10 | Exponential and trigonometric functions |
Keywords:
Appell polynomials; Legendre polynomials; Legendre-Appell polynomials; fractional operators; operational rules; determinant definitionReferences:
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