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1: Bibliography S

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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations. SIAM J. Math. Anal. 10 (4), pp. 823–838.

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External Links:

ISSN 0036-1410, Document, MathReview (Ernest G. Kalnins), ZentralBlatt

Referenced by:

§28.32(i).

Encodings:

BibTeX

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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions. J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.

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Notes:

Includes Fortran code, maximum accuracy 18S.

External Links:

MathReview (Martin E. Price), ZentralBlatt

Referenced by:

§6.21(ii).

Encodings:

BibTeX

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Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.

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External Links:

MathReview (H. Bateman), ZentralBlatt

Referenced by:

§28.1, 7th item, Notations S, Notations S.

Encodings:

BibTeX

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Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients. Technology Press of M. I. T. and John Wiley & Sons, Inc., New York.

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External Links:

ISBN 0262190028, 0262692910, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

1st item, Ch.30.

Encodings:

BibTeX

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2: 35.12 Software

… ►References to research software that is available in other ways is listed separately. …

3: Vadim B. Kuznetsov

… ►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. …

4: 28.32 Mathematical Applications

… ►The separated solutions $V(\xi ,\eta )=v(\xi )w(\eta )$ can be obtained from the modified Mathieu’s equation (28.20.1) for $v$ and from Mathieu’s equation (28.2.1) for $w$, where $a$ is the separation constant and $q=\frac{1}{4}{c}^2{k}^2$. … ► … ►Kernels $K$ can be found, for example, by separating solutions of the wave equation in other systems of orthogonal coordinates. … ►is separated in this system, each of the separated equations can be reduced to the Whittaker–Hill equation (28.31.1), in which $A,B$ are separation constants. …

5: Charles W. Clark

… ►He has been a Visiting Fellow at the Australian National University, a Dr. Lee Fellow at Christ Church College of the University of Oxford, and Visiting Professor at the National University of Singapore. …

6: 16.27 Software

… ►References to research software that is available in other ways is listed separately. …

7: 26.22 Software

… ►References to research software that is available in other ways is listed separately. …

8: 34.15 Software

… ►References to research software that is available in other ways is listed separately. …

9: Howard S. Cohl

… ►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 $q$-series. …

10: 31.17 Physical Applications

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§31.17(i) Addition of Three Quantum Spins

►The problem of adding three quantum spins $𝐬$, $𝐭$, and $𝐮$ 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 ${𝐉}^2$ and ${𝐻}_s$ admit separation of variables in $z_1,z_2$, leading to the following factorization of the eigenfunction $\mathrm{\Psi }(𝐱)$: … ►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). …