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11—20 of 85 matching pages
11: 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.
12: 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.
13: Peter A. Clarkson
14: Hans Volkmer
15: Bibliography
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Unsteady lifting-line theory as a singular-perturbation problem.
J. Fluid Mech 153, pp. 59–81.
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Some orthogonal -polynomials.
Math. Nachr. 30, pp. 47–61.
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Bailey’s Transform, Lemma, Chains and Tree.
In Special Functions 2000: Current Perspective and Future
Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.),
NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.
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Note on the trivial zeros of Dirichlet -functions.
Proc. Amer. Math. Soc. 94 (1), pp. 29–30.
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Critical points of smooth functions, and their normal forms.
Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).
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16: 24.1 Special Notation
17: Bibliography F
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Computation of complex Airy functions and their zeros using asymptotics and the differential equation.
ACM Trans. Math. Software 30 (4), pp. 471–490.
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Algorithm 838: Airy functions.
ACM Trans. Math. Software 30 (4), pp. 491–501.
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The third Appell function for one large variable.
J. Approx. Theory 165, pp. 60–69.
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Complex roots of , , and
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Math. Comp. 30 (135), pp. 541–545.
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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions.
Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.
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18: Bibliography T
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LSFBTR: A subroutine for calculating spherical Bessel transforms.
Comput. Phys. Comm. 30 (1), pp. 93–99.
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An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives.
J. Comput. Phys. 32 (2), pp. 270–279.
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The numerical computation of the confluent hypergeometric function
.
Numer. Math. 41 (1), pp. 63–82.
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Über die Lamésche Differentialgleichung.
Math. Nachr. 30, pp. 137–154 (German).
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