zonal spherical harmonics
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11—20 of 110 matching pages
11: 35.9 Applications
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►In chemistry, Wei and Eichinger (1993) expresses the probability density functions of macromolecules in terms of generalized hypergeometric functions of matrix argument, and develop asymptotic approximations for these density functions.
►In the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998).
12: 29.18 Mathematical Applications
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►(29.18.5) is the differential equation of spherical Bessel functions (§10.47(i)), and (29.18.6), (29.18.7) agree with the Lamé equation (29.2.1).
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§29.18(iii) Spherical and Ellipsoidal Harmonics
…13: 10.73 Physical Applications
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§10.73(ii) Spherical Bessel Functions
►The functions , , , and arise in the solution (again by separation of variables) of the Helmholtz equation in spherical coordinates (§1.5(ii)): …With the spherical harmonic defined as in §14.30(i), the solutions are of the form with , , , or , depending on the boundary conditions. Accordingly, the spherical Bessel functions appear in all problems in three dimensions with spherical symmetry involving the scattering of electromagnetic radiation. …14: 1.17 Integral and Series Representations of the Dirac Delta
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Bessel Functions and Spherical Bessel Functions (§§10.2(ii), 10.47(ii))
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1.17.14
, .
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1.17.22
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Spherical Harmonics (§14.30)
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1.17.25
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15: 10.55 Continued Fractions
§10.55 Continued Fractions
►For continued fractions for and see Cuyt et al. (2008, pp. 350, 353, 362, 363, 367–369).16: Bibliography L
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Exact operator solution of the Calogero-Sutherland model.
Comm. Math. Phys. 178 (2), pp. 425–452.
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Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Comput. Phys. Comm. 99 (2-3), pp. 297–306.
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Computations of spheroidal harmonics with complex arguments: A review with an algorithm.
Phys. Rev. E 58 (5), pp. 6792–6806.
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17: 10.48 Graphs
18: Bibliography Z
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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Tables and formulae for the spherical functions
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Translated by E. L. Albasiny, Pergamon Press, Oxford.
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