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Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method

 

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Opened Access Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method
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Author: Santos Cardoso, José Luis dos
Fernandes, Cibele M.
Álvarez Nodarse, Renato
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009
Published in: Electronic transactions on numerical analysis, 35, 17-39.
Document type: Article
Abstract: The functions of hypergeometric-type are the solutions y = yν(z) of the differential equation σ(z)y ′′ + τ(z)y ′ + λy = 0, where σ and τ are polynomials of degrees not higher than 2 and 1, respectively, and λ is a constant. Here we consider a class of functions of hypergeometric type: those that satisfy the condition λ + ντ′ + 1 2 ν(ν − 1)σ ′′ = 0, where ν is an arbitrary complex (fixed) number. We also assume that the coefficients of the polynomials σ and τ do not depend on ν. To this class of functions belong Gauss, Kummer, and Hermite functions, and also the classical orthogonal polynomials. In this work, using the constructive approach introduced by Nikiforov and Uvarov, several structural properties of the hypergeometric-type functions y = yν (z) are obtained. Applications to hypergeometric functions and classical orthogonal polynomials are also given.
Cite: Santos Cardoso, J.L.d., Fernandes, C.M. y Álvarez Nodarse, R. (2009). Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method. Electronic transactions on numerical analysis, 35, 17-39.
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URI: http://hdl.handle.net/11441/41720

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