Geodesic
Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 17-39.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The functions of hypergeometric-type are the solutions y = y$\nu (z)$ of the differential equation $\sigma (z)y^{\prime}$^prime + tau(z)y^prime + lambday = 0, where sigmaand tauare polynomials of degrees not higher than 2 and 1, respectively, and lambdais a constant. Here we consider a class of functions of hypergeometric type: those that satisfy the condition lambda+ nutau^prime + 1 nu(nu- 1)sigma^prime$^{\prime} = $0, where nuis an arbitrary complex (fixed) number. We also assume that the coefficients 2 of the polynomials sigmaand taudo not depend on nu. To this class of functions belong Gauss, Kummer, and Hermite functions, and also the classical orthogonal polynomials. In this work, using the constructive approach introduced by Nikiforov and Uvarov, several structural properties of the hypergeometric-type functions y = ynu$(z)$ are obtained.
Classification : 33C45, 33C05, 33C15
Keywords: hypergeometric-type functions, recurrence relations, classical orthogonal polynomials 
@article{ETNA_2009__35__a14,
     author = {Cardoso, J.L. and Fernandes, C.M. and \'Alvarez-Nodarse, R.},
     title = {Structural and recurrence relations for hypergeometric-type functions by {Nikiforov-Uvarov} method},
     journal = {Electronic transactions on numerical analysis},
     pages = {17--39},
     publisher = {mathdoc},
     volume = {35},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a14/}
}
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Cardoso, J.L.; Fernandes, C.M.; Álvarez-Nodarse, R. Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method. Electronic transactions on numerical analysis, Tome 35 (2009), pp. 17-39. http://geodesic.mathdoc.fr/item/ETNA_2009__35__a14/