A method for the approximation of functions defined by formal series expansions in orthogonal polynomials-Reference-Cited by-同舟云学术

A method for the approximation of functions defined by formal series expansions in orthogonal polynomials

Published:1969 Issue:106 Volume:23 Page:275-287
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Holdeman Jonas T.

Abstract

An algorithm is described for numerically evaluating functions defined by formal (and possibly divergent) series as well as convergent series of orthogonal functions which are, apart from a factor, orthogonal polynomials. When the orthogonal functions are polynomials, the approximations are rational functions. The algorithm is similar in some respects to the method of Padé approximants. A rational approximation involving Tchebychev polynomials due to H. Maehley and described by E. Kogbetliantz [1] is a special case of the algorithm.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1969-23-106/S0025-5718-1969-0251412-1/S0025-5718-1969-0251412-1.pdf

Reference6 articles.

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2. A. Erdélyi, et al., Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, 1953. MR 15, 419.

3. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 1, 14.

4. Legendre polynomial expansions of hypergeometric functions with applications;Holdeman, Jonas T., Jr.;J. Mathematical Phys.,1970

5. An investigation of the applicability of the Padé approximant method;Baker, George A., Jr.;J. Math. Anal. Appl.,1961

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