Extraction of orthogonal polynomials from generating function for reciprocal of odd numbers

P. Shashikala ()
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P. Shashikala: University of Mysore

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 177-185

Abstract: Abstract In the present paper the orthogonality relations, exhibited by both numerator and denominator polynomials of both even and odd order convergents of a regular C-fraction of a power series with coefficients as reciprocal of odd numbers are described. The two sequences of convergents are nothing but diagonal and upper diagonal Pade approximants for the power series. The two orthogonal polynomials extracted from denominators are shown to be classical orthogonal polynomials and two orthogonal polynomials extracted from numerators are shown to be non-classical orthogonal polynomials..

Keywords: Combinatorial enumeration problems; continued fractions and generalizations; continued fractions (function-theoretic results); orthogonal polynomials and functions of hypergeometric type; other special orthogonal polynomials and functions and Pade approximation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-017-0220-0

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