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

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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].

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Beograd, Serbia & University of Niš, Faculty of Sciences and Mathematics, P.O. Box 224, 18000, Niš, Serbia

    Gradimir V. Milovanović

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  1. Gradimir V. Milovanović
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Correspondence to Gradimir V. Milovanović.

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Milovanović, G.V. A Note on Extraction of Orthogonal Polynomials from Generating Function for Reciprocal of Odd Numbers. Indian J Pure Appl Math 50, 15–22 (2019). https://doi.org/10.1007/s13226-019-0303-1

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  • DOI: https://doi.org/10.1007/s13226-019-0303-1

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