Alternative Jacobi Polynomials and Orthogonal Exponentials

Details Alternative Jacobi Polynomials and Orthogonal Exponentials Alternative Jacobi Polynomials and Orthogonal Exponentials

2011-05-10

arxiv.org/abs/1105.1838v1

Mathematics

Classical Analysis and ODEs

11 pages, 2 figures

Scientific paper

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.

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