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1: 34.5 Basic Properties: Symbol
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34.5.8
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34.5.13
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34.5.19
odd, ,
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34.5.20
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►Equation (34.5.23) can be regarded as an alternative definition of the symbol.
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2: 34.1 Special Notation
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►An often used alternative to the symbol is the Clebsch–Gordan coefficient
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nonnegative integers. | |
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34.1.1
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3: 34.2 Definition: Symbol
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34.2.1
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34.2.2
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34.2.5
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34.2.6
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►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26).
4: 34.4 Definition: Symbol
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34.4.1
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34.4.2
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34.4.3
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►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).
5: 34.8 Approximations for Large Parameters
6: 18.39 Applications in the Physical Sciences
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►Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced.
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§18.39(iii) Non Classical Weight Functions of Utility in DVR Method in the Physical Sciences
… ►Table 18.39.1 lists typical non-classical weight functions, many related to the non-classical Freud weights of §18.32, and §32.15, all of which require numerical computation of the recursion coefficients (i. …Shizgal (2015, Chapter 2), contains a broad-ranged discussion of methods and applications for these, and other, non-classical weight functions. … ►where is a real, positive, scaling factor, and a non-negative integer. …7: 34.3 Basic Properties: Symbol
8: 18.38 Mathematical Applications
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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions
►The basic ideas of Gaussian quadrature, and their extensions to non-classical weight functions, and the computation of the corresponding quadrature abscissas and weights, have led to discrete variable representations, or DVRs, of Sturm–Liouville and other differential operators. …Each of these typically require a particular non-classical weight functions and analysis of the corresponding OP’s. … ►The symbol (34.2.6), with an alternative expression as a terminating of unit argument, can be expressed in terms of Hahn polynomials (18.20.5) or, by (18.21.1), dual Hahn polynomials. … ►Non-Classical Weight Functions
…9: 12.15 Generalized Parabolic Cylinder Functions
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►This equation arises in the study of non-self-adjoint elliptic boundary-value problems involving an indefinite weight function.
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