Pollaczek polynomials and hypergeometric representation

This paper gives a solution, without the use of the three-term recurrence relation, of the problem posed in Ismail (Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge, 2005 ) (Problem 24.8.2, p. 658): that the hypergeometric representation of the gene...

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Bibliographic Details
Published in:The Ramanujan journal 2013-04, Vol.30 (3), p.399-402
Main Authors: Benameur, Jamel, Blel, Mongi
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Summary:This paper gives a solution, without the use of the three-term recurrence relation, of the problem posed in Ismail (Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge, 2005 ) (Problem 24.8.2, p. 658): that the hypergeometric representation of the general Pollaczek polynomials is a polynomial in cos( θ ) of degree n . Chu solved in (Ramanujan J. 13(1–3): 221–225, 2007 ) the problem in a particular case. We use elementary properties of functions of complex variables and Pfaff’s transformation on hypergeometric 2 F 1 -series.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-012-9405-7