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8 matching pages
1: 10.75 Tables
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Makinouchi (1966) tabulates all values of and in the interval , with at least 29S. These are for , 10, 20; , ; with and , except for .
2: Bibliography I
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The zeros of regular Coulomb wave functions and of their derivatives.
Math. Comp. 29, pp. 878–887.
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An integral which occurs in statistics.
Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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3: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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►Table 26.4.1 gives numerical values of multinomials and partitions for .
…For each all possible values of are covered.
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4: 25.12 Polylogarithms
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►Other notations and names for include (Kölbig et al. (1970)), Spence function (’t Hooft and Veltman (1979)), and (Maximon (2003)).
►In the complex plane has a branch point at .
The principal branch has a cut along the interval and agrees with (25.12.1) when ; see also §4.2(i).
The remainder of the equations in this subsection apply to principal branches.
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►For other values of , is defined by analytic continuation.
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5: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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27.2.3
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27.2.4
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27.2.14
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6: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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Algorithm 537: Characteristic values of Mathieu’s differential equation.
ACM Trans. Math. Software 5 (1), pp. 112–117.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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Lie algebraic approaches to classical partition identities.
Adv. in Math. 29 (1), pp. 15–59.
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7: Bibliography O
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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one.
Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Bessel Functions. Part III: Zeros and Associated Values.
Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.
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Error bounds for stationary phase approximations.
SIAM J. Math. Anal. 5 (1), pp. 19–29.
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Modified quotients of cylinder functions.
Math. Tables Aids Comput. 10, pp. 27–28.
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8: Bibliography G
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A continued fraction algorithm for the computation of higher transcendental functions in the complex plane.
Math. Comp. 21 (97), pp. 18–29.
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Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions.
ACM Trans. Math. Software 28 (3), pp. 325–336.
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Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions.
ACM Trans. Math. Software 28 (4), pp. 436–447.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Painlevé Differential Equations in the Complex Plane.
Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin-New York.
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