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Four Orthogonal Polynomials Connected to e-x


Affiliations
1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India
     

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In the present paper the orthogonality relations, exhibited by both numerator and denominator polynomials of both [n/n] and [n−1/n] Pade approximants for power series expansion of e-x, given by regular C-fraction expansion, are described. The four orthogonal polynomials thus derived are shown to form classical orthogonal polynomials.

Keywords

Pade Approximants, Regular C-Fraction, Exponential Function, Classical Orthogonal Polynomials.
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  • Four Orthogonal Polynomials Connected to e-x

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Authors

R. Rangarajan
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India
P. Shashikala
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India

Abstract


In the present paper the orthogonality relations, exhibited by both numerator and denominator polynomials of both [n/n] and [n−1/n] Pade approximants for power series expansion of e-x, given by regular C-fraction expansion, are described. The four orthogonal polynomials thus derived are shown to form classical orthogonal polynomials.

Keywords


Pade Approximants, Regular C-Fraction, Exponential Function, Classical Orthogonal Polynomials.