STRUCTURAL AND RECURRENCE RELATIONS FOR HYPERGEOMETRIC-TYPE FUNCTIONS BY NIKIFOROV-UVAROV METHOD

The functions of hypergeometric-type are the solutions y = y(nu)(z) of the differential equation sigma(z)y '' + tau(z)y' + lambda y = 0, where sigma and tau are polynomials of degrees not higher than 2 and 1, respectively, and lambda is a constant. Here we consider a class of functions of hypergeometric type: those that satisfy the condition lambda + nu tau' + 1/2 nu(nu - 1)sigma '' = 0, where nu is an arbitrary complex (fixed) number. We also assume that the coefficients of the polynomials sigma and tau do 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 = y(nu)(z) are obtained. Applications to hypergeometric functions and classical orthogonal polynomials are also given.