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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.