ellipsoidal%20harmonics
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11—20 of 128 matching pages
11: Bibliography C
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On the expansion of a Coulomb potential in spherical harmonics.
Proc. Cambridge Philos. Soc. 46, pp. 626–633.
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Ellipsoidal distributions of charge or mass.
J. Mathematical Phys. 2, pp. 441–450.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Demagnetization factors for general ellipsoids.
J. Appl. Phys. 70 (6), pp. 2911–2914.
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12: 20 Theta Functions
Chapter 20 Theta Functions
…13: 17.17 Physical Applications
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►See Kassel (1995).
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►It involves -generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials.
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14: Bibliography G
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A harmonic mean inequality for the gamma function.
SIAM J. Math. Anal. 5 (2), pp. 278–281.
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A code to evaluate prolate and oblate spheroidal harmonics.
Comput. Phys. Comm. 108 (2-3), pp. 267–278.
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Evaluation of toroidal harmonics.
Comput. Phys. Comm. 124 (1), pp. 104–122.
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DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics.
Comput. Phys. Comm. 139 (2), pp. 186–191.
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
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15: 25.11 Hurwitz Zeta Function
16: Donald St. P. Richards
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►Richards has published numerous papers on special functions of matrix argument, harmonic analysis, multivariate statistical analysis, probability inequalities, and applied probability.
He is editor of the book Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, published by the American Mathematical Society in 1992, and coeditor of Representation Theory and Harmonic Analysis: A Conference in Honor of R. A. Kunze (with T.
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17: 30.14 Wave Equation in Oblate Spheroidal Coordinates
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►The coordinate surfaces are oblate ellipsoids of revolution with focal circle , .
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§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
►Equation (30.13.7) for together with the boundary condition on the ellipsoid given by , poses an eigenvalue problem with as spectral parameter. …18: 18.39 Applications in the Physical Sciences
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► a) The Harmonic Oscillator
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►This is illustrated in Figure 18.39.1 where the first and fourth excited state eigenfunctions of the Schrödinger operator with the rationally extended harmonic potential, of (18.39.19), are shown, and compared with the first and fourth excited states of the harmonic oscillator eigenfunctions of (18.39.14) of paragraph a), above.
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►The eigenfunctions of are the spherical harmonics
with eigenvalues , each with degeneracy as .
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►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
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19: 30.13 Wave Equation in Prolate Spheroidal Coordinates
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►The coordinate surfaces are prolate ellipsoids of revolution with foci at , .
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§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
►Equation (30.13.7) for , and subject to the boundary condition on the ellipsoid given by , poses an eigenvalue problem with as spectral parameter. …For the Dirichlet boundary-value problem of the region between two ellipsoids, the eigenvalues are determined from …20: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Integral equations and relations for Lamé functions and ellipsoidal wave functions.
Proc. Cambridge Philos. Soc. 64, pp. 113–126.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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