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21—30 of 661 matching pages
21: Frank W. J. Olver
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►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the online NIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).
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22: About the Project
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►They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web.
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23: Bibliography D
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Detection of the density matrix through optical homodyne tomography without filtered back projection.
Phys. Rev. A 50 (5), pp. 4298–4302.
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Bernoulli Numbers. Bibliography (1713–1990).
Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.
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Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält.
Abhandlungen der Königlich Preussischen Akademie der
Wissenschaften von 1837, pp. 45–81 (German).
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Über die Bestimmung der mittleren Werthe in der Zahlentheorie.
Abhandlungen der Königlich Preussischen Akademie der
Wissenschaften von 1849, pp. 69–83 (German).
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On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function.
Methods Appl. Anal. 5 (3), pp. 223–247.
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24: 1.3 Determinants, Linear Operators, and Spectral Expansions
25: 35.2 Laplace Transform
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►where the integration variable ranges over the space .
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►Then (35.2.1) converges absolutely on the region , and is a complex analytic function of all elements of .
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►Assume that converges, and also that its limit as is .
…where the integral is taken over all such that and ranges over
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►If is the Laplace transform of , , then is the Laplace transform of the convolution , where
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26: Bibliography O
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Computing : The combinatorial method.
Revista do DETUA 4 (6), pp. 759–768.
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Associated Legendre functions on the cut.
J. Comput. Phys. 51 (3), pp. 502–518.
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Numerical solution of second-order linear difference equations.
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
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Error Analysis of Complex Arithmetic.
In Computational Aspects of Complex Analysis (Braunlage, 1982), H. Werner, L. Wuytack, E. Ng, and H. J. Bünger (Eds.),
NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Vol. 102, pp. 279–292.
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Spectral decomposition of tent maps using symmetry considerations.
J. Statist. Phys. 84 (1-2), pp. 269–276.
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27: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►With denoting here the elementary charge, the Coulomb potential between two point particles with charges and masses separated by a distance is , where are atomic numbers, is the electric constant, is the fine structure constant, and is the reduced Planck’s constant.
The reduced mass is , and at energy of relative motion with relative orbital angular momentum , the Schrödinger equation for the radial wave function is given by
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►For and , the electron mass, the scaling factors in (33.22.5) reduce to the Bohr radius, , and to a multiple of the Rydberg constant,
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►The penetrability of repulsive Coulomb potential barriers is normally expressed in terms of the quantity (Mott and Massey (1956, pp. 63–65)).
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28: 18.39 Applications in the Physical Sciences
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►where is a spatial coordinate, the mass of the particle with potential energy , is the reduced Planck’s constant, and a finite or infinite interval.
►Here the term represents the quantum kinetic energy of a single particle of mass , and its potential energy.
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►and , has eigenfunctions
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►The eigenfunctions of are the spherical harmonics with eigenvalues , each with degeneracy as .
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►, , Mohr and Taylor (2005, Table XXX, p. 71), where the relationship of to SI units is spelled out.
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29: Bibliography W
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Two tables of partitions.
Proc. London Math. Soc. (2) 42, pp. 550–556.
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Surface Waves.
In Handbuch der Physik, Vol. 9, Part 3,
pp. 446–778.
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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules.
Ann. Inst. Statist. Math. 45 (3), pp. 467–475.
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Harmonic Analysis.
In Studies in Real and Complex Analysis, I. I. Hirschman (Ed.),
Studies in Mathematics, Vol. 3, pp. 124–178.
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Asymptotics for the polynomials.
J. Approx. Theory 66 (1), pp. 58–71.
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30: Richard A. Askey
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►Over his career his primary research areas were in Special Functions and Orthogonal Polynomials, but also included other topics from Classical Analysis and related areas.
His well-known book Special Functions (with G.
…Another significant contribution was the Askey-Gasper inequality for Jacobi polynomials which was published in Positive Jacobi polynomial sums. II (with G.
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► Schempp), published by Reidel Publishing Company in 1984, Ramanujan Revisited (with G.
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