Institute of Physics Ministry of Science and Education Republic of Azerbaijan

TWO NEW LIMIT TRANSITIONS FROM JACOBI POLYNOMIALS TO HERMITE POLYNOMIALS

Shakir M. Nagiyev

ABSTRACT

We present two new limit relations that reduce the orthogonal Jacobi polynomials directly to the Hermite polynomials with shifted and nonshifted arguments. The proofs of these limit relations are based on the method of mathematical induction. The obtained limits open the way to studying new exactly solvable harmonic oscillator models in quantum mechanics in terms of Jacobi polynomials.

Keywords: Jacobi polynomials, Hermite polynomials, limit relations.
DOI:10.70784/azip.1.2025303

Received: 20.05.2025
Internet publishing: 07.07.2025 AJP Fizika E 2025 03 en p.03-08

AUTHORS & AFFILIATIONS

Institute of Physics Ministry of Science and Education of the Republic of Azerbaijan, 131 H. Javid Ave., Baku, AZ-1073, Azerbaijan
E-mail: shakir.m.nagiyev@gmail.com

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