separation constants
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31—35 of 35 matching pages
31: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►Note that the integral in (1.18.66) is not singular if approached separately from above, or below, the real axis: in fact analytic continuation from the upper half of the complex plane, across the cut, and onto higher Riemann Sheets can access complex poles with singularities at discrete energies corresponding to quantum resonances, or decaying quantum states with lifetimes proportional to .
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32: Bibliography B
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Constant mean curvature surfaces and integrable equations.
Uspekhi Mat. Nauk 46 (4(280)), pp. 3–42, 192 (Russian).
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Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation.
J. Phys. A 30 (2), pp. 559–571.
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33: Bibliography P
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Tables of the Incomplete -function.
Biometrika Office, Cambridge University Press, Cambridge.
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A K Peters Ltd., Wellesley, MA.
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34: 17.6 Function
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17.6.28
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►where , , and the contour of integration separates the poles of from those of , and the infimum of the distances of the poles from the contour is positive.
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35: 2.1 Definitions and Elementary Properties
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►(Here and elsewhere in this chapter is an arbitrary small positive constant.)
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►For example, suppose is continuous and as in , where () is a constant.
Then
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2.1.12
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►In those cases it is usually necessary to interpret each infinite series separately in the manner described above; that is, it is not always possible to reinterpret the asymptotic approximation as a single asymptotic expansion.
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