separable
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1: 35.12 Software
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►References to research software that is available in other ways is listed separately.
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2: Vadim B. Kuznetsov
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►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics.
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3: 28.32 Mathematical Applications
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►The separated solutions can be obtained from the modified Mathieu’s equation (28.20.1) for and from Mathieu’s equation (28.2.1) for , where is the separation constant and .
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►Kernels can be found, for example, by separating solutions of the wave equation in other systems of orthogonal coordinates.
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►is separated in this system, each of the separated equations can be reduced to the Whittaker–Hill equation (28.31.1), in which are separation constants.
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4: 16.27 Software
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►References to research software that is available in other ways is listed separately.
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5: 26.22 Software
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►References to research software that is available in other ways is listed separately.
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6: 34.15 Software
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►References to research software that is available in other ways is listed separately.
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7: Howard S. Cohl
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►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and -series.
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8: 31.17 Physical Applications
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§31.17(i) Addition of Three Quantum Spins
►The problem of adding three quantum spins , , and can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions. … ►The operators and admit separation of variables in , leading to the following factorization of the eigenfunction : … ►For more details about the method of separation of variables and relation to special functions see Olevskiĭ (1950), Kalnins et al. (1976), Miller (1977), and Kalnins (1986). …9: 27.10 Periodic Number-Theoretic Functions
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is separable for some if
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►For any Dirichlet character , is separable for if , and is separable for every if and only if whenever .
For a primitive character , is separable for every , and
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►Conversely, if is separable for every , then is primitive (mod ).
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10: 15.20 Software
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►References to research software that is available in other ways is listed separately.
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