Open AccessDifferential and integral equations for Legendre-Laguerre based hybrid polynomials
Author(s) -
Subuhi Khan,
Mumtaz Riyasat,
Shahid Ahmad Wani
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i3.894
Subject(s) - laguerre polynomials , legendre polynomials , mathematics , classical orthogonal polynomials , hermite polynomials , legendre function , discrete orthogonal polynomials , difference polynomials , laguerre's method , gegenbauer polynomials , orthogonal polynomials , mathematical analysis , associated legendre polynomials , wilson polynomials , differential (mechanical device) , physics , thermodynamics
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.