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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
DOI: https://doi.org/10.1090/S0025-5718-1969-0251412-1
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.


References [Enhancements On Off] (What's this?)

  • [1] E. G. Kogbetliantz, ``Generation of elementary functions,'' in Mathematical Methods for Digital Computers, Wiley, New York, 1960. MR 22 #8681. MR 0117907 (22:8681)
  • [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] J. Holdeman, ``Legendre polynomial expansions of hypergeometric functions with applications.'' (To appear.) MR 0254279 (40:7488)
  • [5] G. A. Baker, Jr., J. L. Gammel & J. G. Wills, ``An investigation of the applicability of the Padé approximant method,'' J. Math. Anal. Appl., v. 2, 1961, pp. 405-418. MR 23 #B3125. MR 0130093 (23:B3125)
  • [6] G. A. Baker, Jr., ``The theory and application of the Padé approximant method,'' in Advances in Theoretical Physics, Vol. I, Academic Press, New York, 1965, pp. 1-58. MR 32 #5253. MR 0187807 (32:5253)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0251412-1
Article copyright: © Copyright 1969 American Mathematical Society

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