Coulomb%20phase%20shift
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11: 33.6 Power-Series Expansions in
§33.6 Power-Series Expansions in
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33.6.1
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33.6.2
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33.6.5
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►Corresponding expansions for can be obtained by combining (33.6.5) with (33.4.3) or (33.4.4).
12: 20 Theta Functions
Chapter 20 Theta Functions
…13: 33.17 Recurrence Relations and Derivatives
14: 33.15 Graphics
§33.15 Graphics
►§33.15(i) Line Graphs of the Coulomb Functions and
► … ►§33.15(ii) Surfaces of the Coulomb Functions , , , and
… ► …15: 18.39 Applications in the Physical Sciences
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The Quantum Coulomb Problem
… ►This is Coulomb’s Law. … ►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. … ►The Relativistic Quantum Coulomb Problem
… ►The Coulomb–Pollaczek Polynomials
…16: 33.18 Limiting Forms for Large
17: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Coulomb phase shift.
American Journal of Physics 47 (8), pp. 683–684.
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Chebyshev approximations for the Coulomb phase shift.
Math. Comp. 24 (111), pp. 671–677.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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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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18: 33.1 Special Notation
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►The main functions treated in this chapter are first the Coulomb radial functions , , (Sommerfeld (1928)), which are used in the case of repulsive Coulomb interactions, and secondly the functions , , , (Seaton (1982, 2002a)), which are used in the case of attractive Coulomb interactions.
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Curtis (1964a):
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Greene et al. (1979):
, .
, , .
19: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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