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1: 3.11 Approximation Techniques
is called a Padé table. … … Any five approximants arranged in the Padé table as …Starting with the first column [ n / 0 ] f , n = 0 , 1 , 2 , , and initializing the preceding column by [ n / - 1 ] f = , n = 1 , 2 , , we can compute the lower triangular part of the table via (3.11.25). …
2: Bibliography W
  • P. Wynn (1966) Upon systems of recursions which obtain among the quotients of the Padé table. Numer. Math. 8 (3), pp. 264–269.
  • 3: 3.9 Acceleration of Convergence
    If s n is the n th partial sum of a power series f , then t n , 2 k = ε 2 k ( n ) is the Padé approximant [ ( n + k ) / k ] f 3.11(iv)). … In Table 3.9.1 values of the transforms t n , 2 k are supplied for …
    Table 3.9.1: Shanks’ transformation for s n = j = 1 n ( - 1 ) j + 1 j - 2 .
    n t n , 2 t n , 4 t n , 6 t n , 8 t n , 10
    4: 33.23 Methods of Computation
    Curtis (1964a, §10) describes the use of series, radial integration, and other methods to generate the tables listed in §33.24. … 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. …
    5: Bibliography
  • A. Abramov (1960) Tables of ln Γ ( z ) for Complex Argument. Pergamon Press, New York.
  • G. E. Andrews, I. P. Goulden, and D. M. Jackson (1986) Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.
  • A. Apelblat (1983) Table of Definite and Infinite Integrals. Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.
  • H. Appel (1968) Numerical Tables for Angular Correlation Computations in α -, β - and γ -Spectroscopy: 3 j -, 6 j -, 9 j -Symbols, F- and Γ -Coefficients. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, Springer-Verlag.
  • F. M. Arscott and I. M. Khabaza (1962) Tables of Lamé Polynomials. Pergamon Press, The Macmillan Co., New York.
  • 6: Bibliography B
  • G. A. Baker and P. Graves-Morris (1996) Padé Approximants. 2nd edition, Encyclopedia of Mathematics and its Applications, Vol. 59, Cambridge University Press, Cambridge.
  • S. L. Belousov (1962) Tables of Normalized Associated Legendre Polynomials. Pergamon Press, The Macmillan Co., Oxford-New York.
  • D. Bierens de Haan (1867) Nouvelles Tables d’Intégrales Définies. P. Engels, Leide.
  • D. Bierens de Haan (1939) Nouvelles Tables d’Intégrales Définies. G.E. Stechert & Co., New York.
  • C. Brezinski (1980) Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.