tempered%20distributions
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11: Errata
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►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions.
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Subsection 1.16(vii)
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Subsection 1.16(viii)
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Chapters 8, 20, 36
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References
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Several changes have been made to
An entire new Subsection 1.16(viii) Fourier Transforms of Special Distributions, was contributed by Roderick Wong.
12: 3.8 Nonlinear Equations
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►For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013).
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3.8.15
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►Consider and .
We have and .
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3.8.16
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13: Sidebar 7.SB1: Diffraction from a Straightedge
14: Funding
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►The NIST DLMF project has been funded, in part, by the Knowledge & Distributed Intelligence Program of the National Science Foundation.
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15: Bibliography O
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Tables of Fourier Transforms and Fourier Transforms of Distributions.
Springer-Verlag, Berlin.
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On the distribution of spacings between zeros of the zeta function.
Math. Comp. 48 (177), pp. 273–308.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Distribution of the partition function modulo
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Ann. of Math. (2) 151 (1), pp. 293–307.
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16: 10.73 Physical Applications
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►Laplace’s equation governs problems in heat conduction, in the distribution of potential in an electrostatic field, and in hydrodynamics in the irrotational motion of an incompressible fluid.
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►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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►The analysis of the current distribution in circular conductors leads to the Kelvin functions , , , and .
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17: 36.5 Stokes Sets
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36.5.4
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36.5.7
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►The distribution of real and complex critical points in Figures 36.5.5 and 36.5.6 follows from consistency with Figure 36.5.1 and the fact that there are four real saddles in the inner regions.
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18: 8 Incomplete Gamma and Related
Functions
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19: 28 Mathieu Functions and Hill’s Equation
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