rational functions
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1: 16.26 Approximations
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►For discussions of the approximation of generalized hypergeometric functions and the Meijer -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).
2: 4.47 Approximations
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§4.47(ii) Rational Functions
…3: 5.19 Mathematical Applications
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§5.19(i) Summation of Rational Functions
►As shown in Temme (1996b, §3.4), the results given in §5.7(ii) can be used to sum infinite series of rational functions. …4: 5.23 Approximations
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§5.23(i) Rational Approximations
… ►§5.23(iii) Approximations in the Complex Plane
►See Schmelzer and Trefethen (2007) for a survey of rational approximations to various scaled versions of . …5: 16.7 Relations to Other Functions
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►Further representations of special functions in terms of
functions are given in Luke (1969a, §§6.2–6.3), and an extensive list of
functions with rational numbers as parameters is given in Krupnikov and Kölbig (1997).
6: 19.2 Definitions
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►Let be a cubic or quartic polynomial in with simple zeros, and let be a rational function of and containing at least one odd power of .
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19.2.1
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19.2.2
►where is a polynomial in while and are rational functions of .
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19.2.3
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7: 3.11 Approximation Techniques
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§3.11(iii) Minimax Rational Approximations
… ►The theory of polynomial minimax approximation given in §3.11(i) can be extended to the case when is replaced by a rational function . … ►Example
… ►The rational function … ►A general procedure is to approximate by a rational function (vanishing at infinity) and then approximate by . …8: Bibliography I
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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9: 17.12 Bailey Pairs
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►A sequence of pairs of rational functions of several variables , , is called a Bailey pair provided that for each
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