Generalized polynomials, operational identities and their applications

By G. Dattoli. 2000

173 citations recorded by the source corpus.

Abstract It is shown that an appropriate combination of methods, relevant to generalized operational calculus and to special functions, can be a very useful tool to treat a large body of problems both in physics and mathematics. We discuss operational methods associated with multivariable Hermite, Laguerre, Legendre, and other polynomials to derive a wealth of identities useful in quantum mechanics, electromagnetism, optics, etc., or to derive new identities between special functions as, e.g., Mehler- or mixed-type generating functions.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f98bafac0e9182cfa6f24707a98b98878b9cc8fc

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Orthogonality properties of the Hermite and related polynomials (2005, background): “(1) can be deﬁned by means of the following operational rule (cf. [ 2]): which was applied by Dattoli et al. [3] in order to reconsider the orthogonality property of the classical Hermite polynomials from a different point of view.”
Hermite-based Appell polynomials: Properties and applications (2009, background): “The importance of the use of operational techniques in the study of special functions and their applications has been recognized by Dattoli and his co-workers, see for example [6–12].”