Differential and integral equations for Legendre – Laguerre based hybrid polynomials
DOI:
https://doi.org/10.37863/umzh.v73i3.894Keywords:
Legendre-Laguerre polynomials, Appell polynomials, Legendre-Laguerre-Appell polynomials, Recurrence relations, Differential equations, Integral equationsAbstract
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.
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