Whittaker equation

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1: 28.32 Mathematical Applications

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§28.32(ii) Paraboloidal 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. …

2: 13.14 Definitions and Basic Properties

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§13.14(i) Differential Equation

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Whittaker’s Equation

… ►Standard solutions are: … ►

§13.14(v) Numerically Satisfactory Solutions

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3: 13.28 Physical Applications

… ►and $V_{\kappa ,\mu }^{(j)}(z)$, $j=1,2$, denotes any pair of solutions of Whittaker’s equation (13.14.1). …

4: 28.31 Equations of Whittaker–Hill and Ince

§28.31 Equations of Whittaker–Hill and Ince

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§28.31(i) Whittaker–Hill Equation

… ►and constant values of $A,B,k$, and $c$, is called the Equation of Whittaker–Hill. …

5: Bibliography U

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Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.

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External Links:

MathReview (R. K. Rathy), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.32(ii).

Encodings:

BibTeX

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6: 28.34 Methods of Computation

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Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation (§28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

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7: 13.27 Mathematical Applications

… ►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i).

8: 23.3 Differential Equations

§23.3 Differential Equations

… ►The lattice roots satisfy the cubic equation … ►

§23.3(ii) Differential Equations and Derivatives

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9: Bibliography

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The Whittaker-Hill equation and the wave equation in paraboloidal co-ordinates. Proc. Roy. Soc. Edinburgh Sect. A 67, pp. 265–276.

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External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.31(ii), §28.32(ii).

Encodings:

BibTeX

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10: 32.10 Special Function Solutions

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§32.10(v) Fifth Painlevé Equation

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