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RECURRENCE RELATIONS FOR DISCRETE HYPERGEOMETRIC FUNCTIONS
"... Abstract. We present a general procedure for nding linear recurrence relations for the solutions of the second order dierence equation of hypergeometric type. Applications to wave functions of certain discrete system are also given. 1. ..."
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Abstract. We present a general procedure for nding linear recurrence relations for the solutions of the second order dierence equation of hypergeometric type. Applications to wave functions of certain discrete system are also given. 1.
The Schrödinger equation
"... Ladder type operators and recurrence relations for the radial wave functions of the Nth dimensional oscillators and hydrogenlike atoms ..."
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Ladder type operators and recurrence relations for the radial wave functions of the Nth dimensional oscillators and hydrogenlike atoms
A ̀ LA CARTE RECURRENCE RELATIONS FOR CONTINUOUS AND DISCRETE HYPERGEOMETRIC FUNCTIONS
"... Abstract. We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometrictype functions not only for the continuous case but also for the discrete and qlinear cases, respectively. Some applications i ..."
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Abstract. We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometrictype functions not only for the continuous case but also for the discrete and qlinear cases, respectively. Some applications in Quantum Physics are discussed.
STRUCTURAL AND RECURRENCE RELATIONS FOR HYPERGEOMETRICTYPE FUNCTIONS BY NIKIFOROVUVAROV METHOD∗
"... Abstract. The functions of hypergeometrictype 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: thos ..."
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Abstract. The functions of hypergeometrictype 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 hypergeometrictype functions y = yν(z) are obtained. Applications to hypergeometric functions and classical orthogonal polynomials are also given. Key words. hypergeometrictype functions, recurrence relations, classical orthogonal polynomials AMS subject classifications. 33C45, 33C05, 33C15 1. Introduction. When