A GENERALIZATION OF LAGUERRE-POLYNOMIALS

The authors study orthogonal polynomials on [0, +infinity) with respect to an inner product involving derivatives that cannot be derived from a weight function. These polynomials can be written as a F-3(3) hypergeometric series and they satisfy a second-order differential equation and a five term recurrence relation. At most one zero of each polynomial is located outside (0, +infinity), the interior of the interval of orthogonality. As a special case Koomwinder's Laguerre polynomials {L(n)alpha,M(x)}n=0+infinity are included.