Pollaczek polynomials and hypergeometric representation

Journal Article

Ameur, Mongi Blel and Jamel Ben . 2013

• نوع عمل المنشور: theoric
• المجلة \ الصحيفة: Ramanujan Journal
• رقم الإصدار السنوي: 30
• الصفحات: 399–402

مستخلص المنشور

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.