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Mathematics of Computation

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

Author: Jonas T. Holdeman
Journal: Math. Comp. 23 (1969), 275-287
MSC: Primary 41.30; Secondary 42.00
MathSciNet review: 0251412
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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.

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Article copyright: © Copyright 1969 American Mathematical Society

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