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1: 4.47 Approximations
§4.47(iii) Padé Approximations
2: 19.38 Approximations
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). …
3: 18.36 Miscellaneous Polynomials
They are related to Hermite–Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. …
4: 3.11 Approximation Techniques
§3.11(iv) Padé Approximations
Any five approximants arranged in the Padé table as … For further information on Padé approximations, see Baker and Graves-Morris (1996, §4.7), Brezinski (1980, pp. 9–39 and 126–177), and Lorentzen and Waadeland (1992, pp. 367–395). …
5: 8.27 Approximations
  • Luke (1975, §4.3) gives Padé approximation methods, combined with a detailed analysis of the error terms, valid for real and complex variables except on the negative real z -axis. See also Temme (1994b, §3).

  • Luke (1975, p. 106) gives rational and Padé approximations, with remainders, for E 1 ( z ) and z - 1 0 z t - 1 ( 1 - e - t ) d t for complex z with | ph z | π .

  • 6: 13.31 Approximations
    §13.31(ii) Padé Approximations
    7: 7.24 Approximations
  • Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for F ( z ) , erf z , erfc z , C ( z ) , and S ( z ) ; approximate errors are given for a selection of z -values.

  • 8: 6.20 Approximations
  • Luke (1969b, pp. 402, 410, and 415–421) gives main diagonal Padé approximations for Ein ( z ) , Si ( z ) , Cin ( z ) (valid near the origin), and E 1 ( z ) (valid for large | z | ); approximate errors are given for a selection of z -values.

  • 9: Bibliography B
  • C. Brezinski (1980) Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
  • 10: 33.23 Methods of Computation
    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. …
    §33.23(vii) WKBJ Approximations
    WKBJ approximations2.7(iii)) for ρ > ρ tp ( η , ) are presented in Hull and Breit (1959) and Seaton and Peach (1962: in Eq. …Seaton (1984) estimates the accuracies of these approximations. Hull and Breit (1959) and Barnett (1981b) give WKBJ approximations for F 0 and G 0 in the region inside the turning point: ρ < ρ tp ( η , ) .