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february 2013 Orthogonality of the Meixner-Pollaczek polynomials beyond Favard's theorem
Samuel G. Moreno, Esther M. García-Caballero
Bull. Belg. Math. Soc. Simon Stevin 20(1): 133-143 (february 2013). DOI: 10.36045/bbms/1366306719


We extend the family of Meixner-Pollaczek polynomials $\{P_n^{(\lambda)}(\cdot;\phi)\}_{n=0}^{\infty}$, classically defined for $\lambda>0$ and $0<\phi<\pi$, to arbitrary complex values of the parameter $\lambda$, in such a way that both polynomial systems (the classical and the new {\it generalized} ones) share the same three term recurrence relation. The values $\lambda_N=(1-N)/2$, with $N$ a positive integer, are the only ones for which no orthogonality condition can be deduced from Favard's theorem. In this paper we introduce a non-standard discrete-continuous inner product with respect to which the generalized Meixner-Pollaczek polynomials $\{P_n^{(\lambda_N)}(\cdot;\phi)\}_{n=0}^{\infty}$ become orthogonal.


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Samuel G. Moreno. Esther M. García-Caballero. "Orthogonality of the Meixner-Pollaczek polynomials beyond Favard's theorem." Bull. Belg. Math. Soc. Simon Stevin 20 (1) 133 - 143, february 2013.


Published: february 2013
First available in Project Euclid: 18 April 2013

zbMATH: 1270.33005
MathSciNet: MR3082748
Digital Object Identifier: 10.36045/bbms/1366306719

Primary: 33C45, 42C05

Rights: Copyright © 2013 The Belgian Mathematical Society


Vol.20 • No. 1 • february 2013
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