Laguerre polynomials as Jensen polynomials of Laguerre–Pólya entire functions

Jensen Polynomials and the Turan and Laguerre Inequalities

Orthogonal Polynomials , L 2 - Spacesand Entire Functions

We show that for determinate measures μ having moments of every order and finite index of determinacy, (i.e., a polynomial p exists for which the measure |p|μ is indeterminate) the space L(μ) consists of entire functions of minimal exponential type in the Cartwright class.

Laguerre and Jacobi polynomials

We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials wi...

Laguerre-type Bell polynomials

We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

Specializations of Generalized Laguerre Polynomials

Three specializations of a set of orthogonal polynomials with “8 different q’s” are given. The polynomials are identified as q-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.