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.
Lamiri and M.Ouni state some characterization theorems for d-orthogonal polynomials
of Hermite, Gould-Hopper and Charlier type polynomials. In [3] Y.Ben Cheikh I. Lamiri and M.Ouni
…
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