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A difference equation approach to Plancherel‐Rotach asymptotics for q ‐orthogonal polynomials
Author(s) -
Ismail Mourad,
Law ChunKong
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12332
Subject(s) - hermite polynomials , mathematics , orthogonal polynomials , classical orthogonal polynomials , jacobi polynomials , wilson polynomials , discrete orthogonal polynomials , gegenbauer polynomials , hahn polynomials , differential equation , difference polynomials , mathematical analysis , pure mathematics
In this paper, we employ a difference equation approach to study the Plancherel‐Rotach asymptotics of q ‐orthogonal polynomials about their largest zeros. Our method for q ‐difference equations is an analogue to the turning point problem for Hermite differential equations. It works well in the toy problems of Stieltjes‐Wigert polynomials and q − 1 ‐Hermite polynomials.