Four Orthogonal Polynomials Connected to e-x


  • University of Mysore, Department of Studies in Mathematics, Mysore, 570006, India


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.


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

Subject Discipline

Mathematical Sciences

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F. Ahmad, The Orthogonal Polynomials and the Pade Approximation, Appl. Math. Mech., 19(7) (1998), 663–668.

G. A. Baker, Essentials of Pade Approximants, Academic Press, New York, 1975.

G. A. Baker and P. Graves-Morris, Pade Approximants, Cambridge University Press, New York, 1996.

A. Branquhinho, A Note on Semi-Classical Orthogonal Polynomials, Bull. Belg. Math. Soc., 3 (1996), 1–12.

C. Brezinski, History of Continued Fractions and Pade Approximants, Springer - Verlag, Berlin Heidelberg, 1991.

T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.

R. Y. Dennis, S. N. Singh and S. P. Singh, On Hypergeometric Functions and Ramanujan’s Continued Fractions, Journal of the Indian Math. Soc., Special Volume on the occasion of the centenary of IMS 1907-2007 (2007), 25–50.

E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

R. Rangarajan and H. Muneer Basha, Numerical - Analytical Methods for Non-linear Diffusion Type Differential Equations of Heat Transfer, Journal of the Indian Math. Soc., 77 (1-4)(2010), 159–166.

L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, New York, 1966.


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