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On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials

Author

Listed:
  • 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)

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.

Suggested Citation

  • Elchin I. Jafarov & Aygun M. Mammadova & Joris Van der Jeugt, 2021. "On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials," Mathematics, MDPI, vol. 9(1), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:1:p:88-:d:474262
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