Abstract
In this paper, we derive a result concerning eigenvector for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. The results given by Radulescu, Mandal and authors follow as special cases of this result. Further using these results, we deduce certain properties of generalized Hermite polynomials and Hermite Tricomi functions.
Highlights
The interplay between differential equations, generalized special functions and Lie theory is useful in applications
Radulescu [8] has discussed some properties of Hermite and Laguerre polynomials [9] using some operators defined on a Lie algebra
Pathan and Khan [7] discussed some properties of two variable Laguerre polynomials (TVLP) studied by Dattoli and Torre [3,4]
Summary
Keywords : Generalized Special Functions, Lie Algebra. The interplay between differential equations, generalized special functions and Lie theory is useful in applications. Radulescu [8] has discussed some properties of Hermite and Laguerre polynomials [9] using some operators defined on a Lie algebra. Further Mandal [6] obtained some properties of simple Bessel polynomials considered by Krall and Frink [5].
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