A difference equation approach to Plancherel‐Rotach asymptotics for   q  ‐orthogonal polynomials | Zendy

Ismail Mourad | Zendy; Law ChunKong | Zendy

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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.

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