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21—30 of 91 matching pages
21: Bibliography I
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The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
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Further investigations into the periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
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22: Bibliography L
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Application of theta functions for numerical evaluation of complete elliptic integrals of the first and second kinds.
Comput. Phys. Comm. 60 (3), pp. 319–327.
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On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions.
Constr. Approx. 10 (1), pp. 15–30.
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23: 4.20 Derivatives and Differential Equations
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24: Bibliography C
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New similarity reductions of the Boussinesq equation.
J. Math. Phys. 30 (10), pp. 2201–2213.
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The Numerical Treatment of Differential Equations.
3rd edition, Die Grundlehren der Mathematischen Wissenschaften, Vol. 60, Springer, Berlin.
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Exact elliptic compactons in generalized Korteweg-de Vries equations.
Complexity 11 (6), pp. 30–34.
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The arithmetic-geometric mean of Gauss.
Enseign. Math. (2) 30 (3-4), pp. 275–330.
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25: 29.21 Tables
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Arscott and Khabaza (1962) tabulates the coefficients of the polynomials in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues for , . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.
26: 31.18 Methods of Computation
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►The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.
27: Peter A. Clarkson
28: Hans Volkmer
29: 12.12 Integrals
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►For compendia of integrals see Erdélyi et al. (1953b, v. 2, pp. 121–122), Erdélyi et al. (1954a, b, v. 1, pp. 60–61, 115, 210–211, and 336;
v. 2, pp. 76–80, 115, 151, 171, and 395–398), Gradshteyn and Ryzhik (2000, §7.7), Magnus et al. (1966, pp. 330–331), Marichev (1983, pp. 190–191), Oberhettinger (1974, pp. 144–145), Oberhettinger (1990, pp. 106–108 and 192), Oberhettinger and Badii (1973, pp. 181–185), Prudnikov et al. (1986b, pp. 36–37, 155–168, 243–246, 289–290, 327–328, 419–420, and 619), Prudnikov et al. (1992a, §3.11), and Prudnikov et al. (1992b, §3.11).
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