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## 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.Comment: 11 pages, 2 figure

Topics: Mathematics - Classical Analysis and ODEs, Mathematics - Numerical Analysis, 33C45
Year: 2011
OAI identifier: oai:arXiv.org:1105.1838