Operational Methods in the Study of Sobolev-Jacobi Polynomials

Nicolas Behr, Giuseppe Dattoli, Gérard H. E. Duchamp, Silvia Licciardi and Karol A. Penson
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Nicolas Behr: Institut de Recherche en Informatique Fondamentale (IRIF), Université Paris-Diderot, F-75013 Paris, France
Giuseppe Dattoli: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
Gérard H. E. Duchamp: Laboratoire d’Informatique de Paris-Nord (LIPN), CNRS UMR 7030, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse, France
Silvia Licciardi: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
Karol A. Penson: Laboratoire de Physique Theorique de la Matière Condensée (LPTMC), CNRS UMR 7600, Sorbonne Universités, Université Pierre et Marie Curie, F-75005 Paris, France

Mathematics, 2019, vol. 7, issue 2, 1-34

Abstract: Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called umbral image technique. Besides providing a class of new formulae for generalized hypergeometric functions and an implementation of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of Sobolev-Jacobi polynomials. Motivated by applications to theoretical chemistry, we moreover present a deep link between generalized normal-ordering techniques introduced by Gurappa and Panigrahi, two-variable Hermite polynomials and our integral-based series transforms. Notably, we thus calculate all K -tuple L -shifted lacunary exponential generating functions for a certain family of Sobolev-Jacobi (SJ) polynomials explicitly.

Keywords: Sobolev-Jacobi polynomials; umbral image techniques; generalized normal-ordering; lacunary generating functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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