Alternative Jacobi Polynomials and Orthogonal Exponentials

2011/05/10 by Vladimir S. Chelyshkov, Chelyshkov, Vladimir S. · 1 citation
Mathematics · #33C45 #Advanced Optimization Algorithms Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1105.1838

openalex publication_date 2011/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sequences of orthogonal polynomials that are alternative to the Jacobi polynomials on the interval [0,1] are defined and their properties are established. An (α,β)-parameterized system of orthogonal polynomials of the exponential function on the semi-axis [0,∞) is presented. Two subsystems of the alternative Jacobi polynomials, as well as orthogonal exponential polynomials are described. Two parameterized systems of discretely almost orthogonal functions on the interval [0,1] are introduced.

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