Pollaczek polynomials and hypergeometric representation
Tóm tắt
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.
Tài liệu tham khảo
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Chu, W.: Pollaczek polynomials and hypergeometric representation. Ramanujan J. 13(1–3), 221–225 (2007)
Ismail, M.E.H.: Classical and Quantum Orthogonal Polynomials in One Variable. Encycl. of Math., vol. 98. Cambridge University Press, Cambridge (2005)
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