Padé
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1—10 of 16 matching pages
1: 3.11 Approximation Techniques
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§3.11(iv) Padé Approximations
… ►The array of Padé approximants …is called a Padé table. … … ► …2: 4.47 Approximations
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§4.47(iii) Padé Approximations
…3: 19.38 Approximations
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►Approximations for Legendre’s complete or incomplete integrals of all three kinds, derived by Padé approximation of the square root in the integrand, are given in Luke (1968, 1970).
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4: 7.24 Approximations
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§7.24(iii) Padé-Type Expansions
►Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.
5: 6.20 Approximations
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§6.20(iii) Padé-Type and Rational Expansions
►Luke (1969b, pp. 402, 410, and 415–421) gives main diagonal Padé approximations for , , (valid near the origin), and (valid for large ); approximate errors are given for a selection of -values.
6: 13.31 Approximations
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§13.31(ii) Padé Approximations
►For a discussion of the convergence of the Padé approximants that are related to the continued fraction (13.5.1) see Wimp (1985). …7: 8.27 Approximations
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Luke (1975, p. 106) gives rational and Padé approximations, with remainders, for and for complex with .
8: 8.10 Inequalities
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Padé Approximants
…9: 33.23 Methods of Computation
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►Thompson and Barnett (1985, 1986) and Thompson (2004) use combinations of series, continued fractions, and Padé-accelerated asymptotic expansions (§3.11(iv)) for the analytic continuations of Coulomb functions.
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