A Note on Extraction of Orthogonal Polynomials from Generating Function for Reciprocal of Odd Numbers

Gradimir V. Milovanović ()
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Gradimir V. Milovanović: Serbia & University of Niš, Faculty of Sciences and Mathematics

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 15-22

Abstract: Abstract Motivated by a recent paper by Shashikala [Indian J. Pure Appl. Math. 48 (2) (2017), 177-185] on the extraction four sequences of orthogonal polynomials from generating function from reciprocal of odd numbers, in this note we identify the weight functions and the intervals of orthogonality of these sequences of polynomials. Two of these sequences can be expressed in terms of particular Jacobi polynomials transformed to [0, 1], and other two are non-classical polynomials also orthogonal on [0, 1].

Keywords: Orthogonal polynomials; weight function; recurrence relation; continued fractions; Gauss’s hypergeometric function (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0303-1

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