Coulomb functions with variables r,ϵ
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11—20 of 29 matching pages
11: 33.1 Special Notation
12: 33.19 Power-Series Expansions in
13: 33.4 Recurrence Relations and Derivatives
§33.4 Recurrence Relations and Derivatives
… ►Then, with denoting any of , , or , ►
33.4.2
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33.4.3
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33.4.4
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14: 33.8 Continued Fractions
§33.8 Continued Fractions
… ►
33.8.1
►For , , and see (33.4.1).
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33.8.2
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►If we denote and , then
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15: 33.13 Complex Variable and Parameters
§33.13 Complex Variable and Parameters
►The functions , , and may be extended to noninteger values of by generalizing , and supplementing (33.6.5) by a formula derived from (33.2.8) with expanded via (13.2.42). ►These functions may also be continued analytically to complex values of , , and . The quantities , , and , given by (33.2.6), (33.2.10), and (33.4.1), respectively, must be defined consistently so that … ►
33.13.2
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16: Bibliography D
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Chebyshev series for the spherical Bessel function
.
Comput. Phys. Comm. 18 (1), pp. 73–86.
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Computation of the incomplete gamma function ratios and their inverses.
ACM Trans. Math. Software 12 (4), pp. 377–393.
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Algorithm 708: Significant digit computation of the incomplete beta function ratios.
ACM Trans. Math. Software 18 (3), pp. 360–373.
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Special Functions.
World Scientific Publishing Co., Inc., River Edge, NJ.
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Coulomb wave functions with complex values of the variable and the parameters.
J. Math. Phys. 40 (12), pp. 6145–6166.
17: Bibliography H
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Soft-core Coulomb potentials and Heun’s differential equation.
J. Math. Phys. 51 (2), pp. Art. ID 022107, 19 pages.
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Two-center Coulomb functions.
Comput. Phys. Comm. 103 (2-3), pp. 209–216.
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Calculation of Coulomb wave functions for high energies.
Phys. Rev. 54 (8), pp. 627–628.
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Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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Bessel function expansions of Coulomb wave functions.
J. Math. Phys. 26 (4), pp. 656–659.
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18: Bibliography B
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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy.
Comput. Phys. Comm. 21 (3), pp. 297–314.
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KLEIN: Coulomb functions for real and positive energy to high accuracy.
Comput. Phys. Comm. 24 (2), pp. 141–159.
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COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method.
Comput. Phys. Comm. 27, pp. 147–166.
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The Calculation of Spherical Bessel Functions and Coulomb Functions.
In Computational Atomic Physics: Electron and Positron Collisions
with Atoms and Ions, K. Bartschat and J. Hinze (Eds.),
pp. 181–202.
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Coulomb functions for large charges and small velocities.
Phys. Rev. (2) 97 (2), pp. 542–554.
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19: 18.39 Applications in the Physical Sciences
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c) Spherical Radial Coulomb Wave Functions
… ►The radial Coulomb wave functions , solutions of … ►d) Radial Coulomb Wave Functions Expressed in Terms of the Associated Coulomb–Laguerre OP’s
… ►Discretized and Continuum Expansions of Scattering Eigenfunctions in terms of Pollaczek Polynomials: J-matrix Theory
►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33. …20: Bibliography C
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The hypergeometric function and the -function near their branch points.
Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.
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Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric -functions.
Math. Comp. 75 (255), pp. 1309–1318.
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Coulomb phase shift.
American Journal of Physics 47 (8), pp. 683–684.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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Coulomb Wave Functions.
Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.
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