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.

نوع عمل المنشور

theoric

رقم المجلد

مجلة/صحيفة

Ramanujan Journal

الصفحات

399–402

مزيد من المنشورات