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Wani, Shahid Ahmad; Mallah, Ishfaq Ahmad; Ganie, Javid Ahmad

Fractional calculus and families of generalized Legendre-Laguerre-Appell polynomials. (English) Zbl 1538.33015

Fract. Differ. Calc. 12, No. 2, 133-145 (2022).
Summary: In this article, new families of the generalized Legendre-Laguerre-Appell polynomials are introduced using a combination of operational definitions and integral representations. The integral transformations and the appropriate operational rules are used to obtain the explicit summation equations, determinant definitions, and recurrence relations for the generalised Legendre-Laguerre-Appell polynomials. For the generalized Legendre-Laguerre-Bernoulli, Legendre-Laguerre-Euler, and Legendre-Laguerre-Genocchi polynomials, an equivalent investigation of these findings is offered. Additionally, a number of identities for these polynomials are derived by using suitable 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 definition
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Full Text: DOI

References:

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