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21: 18.40 Methods of Computation
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►Further, exponential convergence in , via the Derivative Rule, rather than the power-law convergence of the histogram methods, is found for the inversion of Gegenbauer, Attractive, as well as Repulsive, Coulomb–Pollaczek, and Hermite weights and zeros to approximate for these OP systems on and respectively, Reinhardt (2018), and Reinhardt (2021b), Reinhardt (2021a).
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22: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable.
2nd edition, McGraw-Hill Book Co., New York.
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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations.
Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
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Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
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Some basic hypergeometric extensions of integrals of Selberg and Andrews.
SIAM J. Math. Anal. 11 (6), pp. 938–951.
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23: 26.9 Integer Partitions: Restricted Number and Part Size
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24: 27.2 Functions
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Table 27.2.1: Primes.
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5 | 11 | 47 | 97 | 149 | 197 | 257 | 313 | 379 | 439 | 499 |
6 | 13 | 53 | 101 | 151 | 199 | 263 | 317 | 383 | 443 | 503 |
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10 | 29 | 71 | 113 | 173 | 229 | 281 | 349 | 409 | 463 | 541 |
25: 34.6 Definition: Symbol
26: Bibliography D
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Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli.
Bull. Sci. Math. (2) 28, pp. 29–32 (French).
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory.
Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
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Algorithm 322. F-distribution.
Comm. ACM 11 (2), pp. 116–117.
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Theta functions and non-linear equations.
Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
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The incomplete beta function—a historical profile.
Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
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27: 5.10 Continued Fractions
28: Bibliography B
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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials.
Math. Comp. 15 (73), pp. 7–11.
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Ramanujan’s theories of elliptic functions to alternative bases.
Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.
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Vortices in Ginzburg-Landau Equations.
In Proceedings of the International Congress of Mathematicians,
Vol. III (Berlin, 1998),
pp. 11–19.
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Theoretical and experimental investigation of the elliptical annual ring antenna.
IEEE Trans. Antennas and Propagation 36 (11), pp. 1526–1530.
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Rainbow over Woolsthorpe Manor.
Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).
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29: 28.6 Expansions for Small
30: Bibliography J
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Some properties of the Erlang loss function.
Bell System Tech. J. 53, pp. 525–551.
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Continued Fractions: Analytic Theory and Applications.
Encyclopedia of Mathematics and its Applications, Vol. 11, Addison-Wesley Publishing Co., Reading, MA.
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The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis.
J. Reine Angew. Math. 583, pp. 29–86.
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