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21—30 of 147 matching pages
21: 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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Note on the addition theorem of parabolic cylinder functions.
J. Indian Math. Soc. (N. S.) 4, pp. 29–30.
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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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22: 28.6 Expansions for Small
23: 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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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions.
IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Exact elliptic compactons in generalized Korteweg-de Vries equations.
Complexity 11 (6), pp. 30–34.
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24: Bibliography O
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Studies on the Painlevé equations. IV. Third Painlevé equation
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Funkcial. Ekvac. 30 (2-3), pp. 305–332.
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Numerical solution of Riemann-Hilbert problems: Painlevé II.
Found. Comput. Math. 11 (2), pp. 153–179.
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Modified quotients of cylinder functions.
Math. Tables Aids Comput. 10, pp. 27–28.
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Algorithm 22: Riccati-Bessel functions of first and second kind.
Comm. ACM 3 (11), pp. 600–601.
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25: Software Index
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11 Struve and Related Functions | |||||||||||||||||||||||||
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28 Mathieu Functions and Hill’s Equation | |||||||||||||||||||||||||
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30 Spheroidal Wave Functions | |||||||||||||||||||||||||
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26: Bibliography F
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Algorithm 838: Airy functions.
ACM Trans. Math. Software 30 (4), pp. 491–501.
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Polynomial relations in the Heisenberg algebra.
J. Math. Phys. 35 (11), pp. 6144–6149.
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On a unified approach to transformations and elementary solutions of Painlevé equations.
J. Math. Phys. 23 (11), pp. 2033–2042.
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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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Algorithm 435: Modified incomplete gamma function.
Comm. ACM 15 (11), pp. 993–995.
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27: 34.7 Basic Properties: Symbol
28: Bibliography L
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An efficient derivative-free method for solving nonlinear equations.
ACM Trans. Math. Software 11 (3), pp. 250–262.
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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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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29: 9.18 Tables
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Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
National Bureau of Standards (1958) tabulates and for and ; for . Precision is 8D.
Gil et al. (2003c) tabulates the only positive zero of , the first 10 negative real zeros of and , and the first 10 complex zeros of , , , and . Precision is 11 or 12S.