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11: 4.24 Inverse Trigonometric Functions: Further Properties
12: Bibliography N
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Elliptic integrals of the second and third kinds.
Zastos. Mat. 11, pp. 99–102.
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On the calculation of elliptic integrals of the second and third kinds.
Zastos. Mat. 11, pp. 91–94.
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Evaluation of negative energy Coulomb (Whittaker) functions.
Comput. Phys. Comm. 159 (1), pp. 55–62.
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The Boutroux ansatz for the second Painlevé equation in the complex domain.
Izv. Akad. Nauk SSSR Ser. Mat. 54 (6), pp. 1229–1251 (Russian).
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13: Bibliography C
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Note on Nörlund’s polynomial
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Proc. Amer. Math. Soc. 11 (3), pp. 452–455.
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Generalized incomplete gamma functions with applications.
J. Comput. Appl. Math. 55 (1), pp. 99–124.
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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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Catastrophes and molecular collisions.
Molecular Phys. 31 (1), pp. 33–55.
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-matrix and -matrix determination of the low-energy and resonance parameters.
Phys. Rev. C 55 (1), pp. 536–539.
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14: 3.9 Acceleration of Convergence
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Table 3.9.1: Shanks’ transformation for .
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►For examples and other transformations for convergent sequences and series, see Wimp (1981, pp. 156–199), Brezinski and Redivo Zaglia (1991, pp. 55–72), and Sidi (2003, Chapters 6, 12–13, 15–16, 19–24, and pp. 483–492).
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2 | 0.82111 11111 11 | 0.82243 44785 14 | 0.82246 61821 45 | 0.82246 70102 48 | 0.82246 70327 79 |
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6 | 0.82239 19390 77 | 0.82246 61352 37 | 0.82246 70190 76 | 0.82246 70331 54 | 0.82246 70334 18 |
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15: Bibliography K
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Über die Wurzeln einiger Zylinderfunktionen und gewisser aus ihnen gebildeter Gleichungen.
Zeitschrift für Mathematik und Physik 54, pp. 55–86 (German).
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Bernstein, Pick, Poisson and related integral expressions for Lambert
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Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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Gravitational field of a spinning mass as an example of algebraically special metrics.
Phys. Rev. Lett. 11 (5), pp. 237–238.
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Algorithm 327: Dilogarithm [S22].
Comm. ACM 11 (4), pp. 270–271.
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16: Bibliography D
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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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Monodromy of certain Painlevé-VI transcendents and reflection groups.
Invent. Math. 141 (1), pp. 55–147.
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The incomplete beta function—a historical profile.
Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
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17: Bibliography P
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Optical properties of layer antiferromagnets with structure.
J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.
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The exact distribution of the Wald statistic.
Econometrica 54 (4), pp. 881–895.
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Numerical calculation of the generalized Fermi-Dirac integrals.
Comput. Phys. Comm. 55 (2), pp. 127–136.
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Algorithm 28. Algorithm for the computation of Bessel function integrals.
J. Comput. Appl. Math. 11 (1), pp. 119–137.
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18: 10.60 Sums
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►For further sums of series of spherical Bessel functions, or modified spherical Bessel functions, see §6.10(ii), Luke (1969b, pp. 55–58), Vavreck and Thompson (1984), Harris (2000), and Rottbrand (2000).
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►See also Watson (1944, Chapters 11 and 16).
19: Bibliography L
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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Higher monotonicity properties of certain Sturm-Liouville functions..
Acta Math. 109, pp. 55–73.
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Algorithm 244: Fresnel integrals.
Comm. ACM 7 (11), pp. 660–661.
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On the theory of Painlevé’s third equation.
Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).
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Algorithms for rational approximations for a confluent hypergeometric function.
Utilitas Math. 11, pp. 123–151.
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20: Bibliography V
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Some Wonderful Formulas an Introduction to Polylogarithms.
In Proceedings of the Queen’s Number Theory Conference, 1979
(Kingston, Ont., 1979), R. Ribenboim (Ed.),
Queen’s Papers in Pure and Appl. Math., Vol. 54, Kingston, Ont., pp. 269–286.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Über die Riemann’sche Primzahlfunction.
Math. Ann. 55, pp. 441–464 (German).
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