On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials

Elchin I. Jafarov, Aygun M. Mammadova and Joris Van der Jeugt
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Elchin I. Jafarov: Institute of Physics, Azerbaijan National Academy of Sciences, Javid av. 131, AZ1143 Baku, Azerbaijan
Aygun M. Mammadova: Institute of Physics, Azerbaijan National Academy of Sciences, Javid av. 131, AZ1143 Baku, Azerbaijan
Joris Van der Jeugt: Department of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium

Mathematics, 2021, vol. 9, issue 1, 1-8

Abstract: In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon 2 F 1 -type hypergeometric transformation formulas, which are applicable to even and odd polynomials separately. This limit opens the way to studying new exactly solvable harmonic oscillator models in quantum mechanics in terms of pseudo-Jacobi polynomials.

Keywords: pseudo-Jacobi polynomials; Hermite polynomials; 2 F 1 -type hypergeometric transformation formulas (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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