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Classification of Laguerre–Hahn orthogonal polynomials of class one
Author(s) -
Filipuk G.,
Rebocho M. N.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800063
Subject(s) - mathematics , orthogonal polynomials , laguerre polynomials , hahn polynomials , classical orthogonal polynomials , discrete orthogonal polynomials , wilson polynomials , class (philosophy) , pure mathematics , recurrence relation , jacobi polynomials , algebra over a field , gegenbauer polynomials , mathematical analysis , artificial intelligence , computer science
We study orthogonal polynomials related to Stieltjes functions satisfying Riccati type differential equations with polynomial coefficients, A S ′ = B S 2 + C S + D , with max { deg ( A ) , deg ( B ) } ≤ 3 , deg ( C ) ≤ 2 . We derive recurrences for the three‐term recurrence relation coefficients of the orthogonal polynomials, including connections with some forms of discrete Painlevé equations.