Alternative Jacobi Polynomials and Orthogonal Exponentials

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 $(\alpha ,\beta )$-parameterized system of orthogonal polynomials of the exponential function on the semi-axis $[0,\infty )$ 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.

11 pages, 2 figures

References in corpus (1)

• A Spectral Method for Solving the Cauchy Problem

Cited by in corpus (4)

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• Spectral Shape Preserving Approximation