Next Article in Journal
Turning Hild’s Sculptures into Single-Sided Surfaces
Previous Article in Journal
Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(2), 124;

Operational Methods in the Study of Sobolev-Jacobi Polynomials

Institut de Recherche en Informatique Fondamentale (IRIF), Université Paris-Diderot, F-75013 Paris, France
ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
Laboratoire d’Informatique de Paris-Nord (LIPN), CNRS UMR 7030, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse, France
Laboratoire de Physique Theorique de la Matière Condensée (LPTMC), CNRS UMR 7600, Sorbonne Universités, Université Pierre et Marie Curie, F-75005 Paris, France
Author to whom correspondence should be addressed.
Received: 3 November 2018 / Revised: 19 January 2019 / Accepted: 22 January 2019 / Published: 24 January 2019
Full-Text   |   PDF [459 KB, uploaded 29 January 2019]


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. View Full-Text
Keywords: Sobolev-Jacobi polynomials; umbral image techniques; generalized normal-ordering; lacunary generating functions Sobolev-Jacobi polynomials; umbral image techniques; generalized normal-ordering; lacunary generating functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Behr, N.; Dattoli, G.; Duchamp, G.H.E.; Licciardi, S.; Penson, K.A. Operational Methods in the Study of Sobolev-Jacobi Polynomials. Mathematics 2019, 7, 124.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top