interior Dirichlet problem

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21: 11.12 Physical Applications

§11.12 Physical Applications

►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …

22: 27.4 Euler Products and Dirichlet Series

§27.4 Euler Products and Dirichlet Series

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27.4.4 $$F(s)=\sum _{n=1}^{\mathrm{\infty }}f(n)n^{-s},$$

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Symbols:

$n$: positive integer, $f$: multiplicative function and $F(s)$: generating function

Permalink:

http://dlmf.nist.gov/27.4.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §27.4 and Ch.27

►called Dirichlet series with coefficients $f(n)$. The function $F(s)$ is a generating function, or more precisely, a Dirichlet generating function, for the coefficients. …

23: 2.10 Sums and Sequences

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On the strip $a\le \mathrm{\Re }z\le n$, $f(z)$ is analytic in its interior, $f^{(2m)}(z)$ is continuous on its closure, and $f(z)=o\left({\mathrm{e}}^{2\pi |\mathrm{\Im }z|}\right)$ as $\mathrm{\Im }z\to \pm \mathrm{\infty }$, uniformly with respect to $\mathrm{\Re }z\in [a,n]$.

… ►These problems can be brought within the scope of §2.4 by means of Cauchy’s integral formula …

24: 28.33 Physical Applications

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§28.33(ii) Boundary-Value Problems

►Physical problems involving Mathieu functions include vibrational problems in elliptical coordinates; see (28.32.1). …The general solution of the problem is a superposition of the separated solutions. … ►

§28.33(iii) Stability and Initial-Value Problems

… ►References for other initial-value problems include: …

25: Bibliography Q

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A note on an open problem about the first Painlevé equation. Acta Math. Appl. Sin. Engl. Ser. 24 (2), pp. 203–210.

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External Links:

ISSN 0168-9673, Document, MathReview (Dmitrii Petrovich Novikov), ZentralBlatt

Referenced by:

§32.11(i).

Encodings:

BibTeX

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On two problems concerning means. J. Hangzhou Inst. Elec. Engrg. 17, pp. 1–7 (Chinese).

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Notes:

In Chinese

Referenced by:

§19.9(i).

Encodings:

BibTeX

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26: 1.9 Calculus of a Complex Variable

… ►Points of a region that are not boundary points are called interior points. … ►

Jordan Curve Theorem

… ►One of these domains is bounded and is called the interior domain of $C$; the other is unbounded and is called the exterior domain of $C$. …

27: 26.20 Physical Applications

… ►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). … ►Other applications to problems in engineering, crystallography, biology, and computer science can be found in Beckenbach (1981) and Graham et al. (1995).

28: 6.17 Physical Applications

… ►Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. …

29: 16.25 Methods of Computation

… ►Instead a boundary-value problem needs to be formulated and solved. …

30: Bibliography X

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Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.

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Notes:

Special issue to celebrate Pierre Sabatier’s 65th birthday (Montpellier, 2000)

External Links:

ISSN 0266-5611, Document, MathReview (Thomas Sauer), ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

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