Uniform asymptotics and zeros of the associated Pollaczek polynomials | Zendy

Huang XiaoMin | Zendy; Wong R. | Zendy

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Uniform asymptotics and zeros of the associated Pollaczek polynomials

Author(s) -

Huang XiaoMin,

Wong R.

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.12292

Subject(s) - mathematics , recurrence relation , classical orthogonal polynomials , orthogonal polynomials , discrete orthogonal polynomials , mathematical analysis

Using a difference‐equation method in a previous paper, we study the associated Pollaczek polynomialsP n λ ( x ; a , b , c )defined by a three‐term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x = 1 + t nwith − ( a + b ) < t and ( a + b ) > 0 , and the other holds for x = 1 + t nwith t in a neighborhood of t = − ( a + b ) . An asymptotic formula is also provided for their largest zeros.

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