A generalization of classical orthogonal polynomials and the convergence of simultaneous Pade approximants

The concept of generalized classical polyorthogonal polynomials and, in particular, that of generalized Laguerre polynomials, corresponding to a collection of measures with supports on infinite rays in the complex plane, is introduced. The asymptotic behavior of these polynomials and of their corresponding functions of the second kind is investigated. Moreover, generalizations of the Bessel functions and of the Euler integral of the second kind are defined and investigated. The convergence of the simultaneous Pade approximants to certain Stieltjes type functions is proved.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 11, pp. 125–165, 1986.