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11—20 of 48 matching pages
11: 34.1 Special Notation
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12: 1.3 Determinants, Linear Operators, and Spectral Expansions
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1.3.2
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13: 30.9 Asymptotic Approximations and Expansions
14: 28.11 Expansions in Series of Mathieu Functions
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►See Meixner and Schäfke (1954, §2.28), and for expansions in the case of the exceptional values of see Meixner et al. (1980, p. 33).
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15: 29.7 Asymptotic Expansions
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29.7.7
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16: Bibliography R
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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials.
Canad. J. Math. 33 (4), pp. 915–928.
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Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics.
Annual Review of Physical Chemistry 33, pp. 223–255.
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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills.
Bell System Tech. J. 33, pp. 417–504.
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17: 23.21 Physical Applications
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18: 28.26 Asymptotic Approximations for Large
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28.26.4
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19: 18.39 Applications in the Physical Sciences
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►The spectrum is mixed, as in §1.18(viii), the positive energy, non-, scattering states are the subject of Chapter 33.
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►Namely for fixed the infinite set labeled by describe only the
bound states for that single , omitting the continuum briefly mentioned below, and which is the subject of Chapter 33, and so an unusual example of the mixed spectra of §1.18(viii).
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►This is also the normalization and notation of Chapter 33 for , and the notation of Weinberg (2013, Chapter 2).
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►As the scattering eigenfunctions of Chapter 33, are not OP’s, their further discussion is deferred to §18.39(iv), where discretized representations of these scattering states are introduced, Laguerre and Pollaczek OP’s then playing a key role.
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►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33.
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