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## 6 matching pages

##### 1: 3.11 Approximation Techniques
is called a Padé table. … … Any five approximants arranged in the Padé table as …Starting with the first column ${[n/0]_{f}}$, $n=0,1,2,\dots$, and initializing the preceding column by ${[n/-1]_{f}}=\infty$, $n=1,2,\dots$, 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 $t_{n,2k}=\varepsilon_{2k}^{(n)}$ is the Padé approximant $[(n+k)/k]_{f}$3.11(iv)). … In Table 3.9.1 values of the transforms $t_{n,2k}$ are supplied for …
##### 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 $\ln\Gamma(z)$ 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 $\alpha$-, $\beta$- and $\gamma$-Spectroscopy: $3j$-, $6j$-, $9j$-Symbols, F- and $\Gamma$-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.