Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered.  2005 Elsevier Inc. All...


 In this paper, the generalized Laguerre-Apostol-Frobenius-type poly-Genocchi polyno- mials of higher order with parameters a, b and c are defined using concept polylogarithm, Laguerre, Apostol Frobenius polynomials. These polynomials possess numerous properties including recurrence relations, explicit formulas certain differential identity. Moreover, some connections these poly- nomials ...

We show that the formalism of hybrid polynomials, interpolating between Hermite and Laguerre polynomials, is very useful in the study of Motzkin numbers and central trinomial coefficients. These sequences are identified as special values of hybrid polynomials, a fact which we use to derive their generalized forms and new identities satisfied by them.

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several generalizations of formula for generalized functions polynomials. As a consequence, give new addition an integral representation these Finally, introduce family Lebesgue spaces show that some special belong to them.

Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials extensions have been introduced investigated. In this paper, we modify the known generating functions polynomials, due to both Milne-Thomsons Dere-Simsek, introduce new class present some involved properties. As obvious special cases newly also power sum-Laguerre-Hermite ...