Authors: Rajković, Predrag
Marinković, Slađana
Stanković, Miomir 
Title: Orthogonal polynomials with varying weight of laguerre type
Journal: Filomat
Volume: 29
Issue: 5
First page: 1053
Last page: 1062
Issue Date: 1-Jan-2015
Rank: M21
ISSN: 0354-5180
DOI: 10.2298/FIL1505053R
In this paper, we define and examine a new functional product in the space of real polynomials. This product includes the weight function which depends on degrees of the participants. In spite of it does not have all properties of an inner product, we construct the sequence of orthogonal polynomials. These polynomials can be eigenfunctions of a differential equation what was used in some considerations in the theoretical physics. In special, we consider Laguerre type weight function and prove that the corresponding orthogonal polynomial sequence is connected with Laguerre polynomials. We study their differential properties and orthogonal properties of some related rational and exponential functions.
Keywords: Differential properties | Functional product | Laguerre polynomials | Orthogonality | Recurrence relations | Weight functions | Zeros
Publisher: University of Niš

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