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11—20 of 242 matching pages
11: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Asymptotic expansion of Mellin transforms in the complex plane.
Int. J. Pure Appl. Math. 71 (3), pp. 465–480.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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12: 8 Incomplete Gamma and Related
Functions
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13: 28 Mathieu Functions and Hill’s Equation
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14: 3.8 Nonlinear Equations
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►These results are also useful in ensuring that no zeros are overlooked when the complex plane is being searched.
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3.8.15
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►Consider and .
We have and .
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►for solving fixed-point problems (3.8.2) cannot always be predicted, especially in the complex plane.
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15: 1.9 Calculus of a Complex Variable
16: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
17: 23 Weierstrass Elliptic and Modular
Functions
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18: 3.4 Differentiation
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►If can be extended analytically into the complex plane, then from Cauchy’s integral formula (§1.9(iii))
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19: 21.10 Methods of Computation
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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.
Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.
20: 26.20 Physical Applications
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►The latter reference also describes chemical applications of other combinatorial techniques.
►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993).
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