Pollaczek polynomials and hypergeometric representation

Ameur, Mongi Blel and Jamel Ben . 2013

This paper gives a solution, without the use of the three-term recurrence

relation, of the problem posed in Ismail (Classical and Quantum Orthogonal Poly-

nomials in One Variable, Cambridge University Press, Cambridge, 2005) (Problem

24.8.2, p. 658): that the hypergeometric representation of the general Pollaczek poly-

nomials 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 F1 -series.

Publication Work Type

theoric

Volume Number

Magazine \ Newspaper

Ramanujan Journal

Pages

399–402

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