A method for the approximation of functions defined by formal series expansions in orthogonal polynomials
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- by Jonas T. Holdeman PDF
- Math. Comp. 23 (1969), 275-287 Request permission
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
- E. G. Kogbetliantz, Generation of elementary functions, Mathematical methods for digital computers, Wiley, New York, 1960, pp. 7–35. MR 0117907 A. Erdélyi, et al., Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, 1953. MR 15, 419. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 1, 14.
- Jonas T. Holdeman Jr., Legendre polynomial expansions of hypergeometric functions with applications, J. Mathematical Phys. 11 (1970), 114–117. MR 254279, DOI 10.1063/1.1665035
- George A. Baker Jr., J. L. Gammel, and John G. Wills, An investigation of the applicability of the Padé approximant method, J. Math. Anal. Appl. 2 (1961), 405–418. MR 130093, DOI 10.1016/0022-247X(61)90019-1
- George A. Baker Jr., The theory and application of the Padé approximant method, Advances in Theoretical Physics, Vol. 1, Academic Press, New York, 1965, pp. 1–58. MR 0187807
Additional Information
- © Copyright 1969 American Mathematical Society
- 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