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1: 28.19 Expansions in Series of ${\mathrm{me}}_{\nu +2n}$ Functions

… ►The series (28.19.2) converges absolutely and uniformly on compact subsets within $S$. …

2: 18.24 Hahn Class: Asymptotic Approximations

… ►With $x=\lambda N$ and $\nu =n/N$, Li and Wong (2000) gives an asymptotic expansion for $K_n(x;p,N)$ as $n\to \mathrm{\infty }$, that holds uniformly for $\lambda$ and $\nu$ in compact subintervals of $(0,1)$. … ►This expansion is uniformly valid in any compact $x$-interval on the real line and is in terms of parabolic cylinder functions. …

3: 21.7 Riemann Surfaces

… ►In almost all applications, a Riemann theta function is associated with a compact Riemann surface. …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. …This compact curve may have singular points, that is, points at which the gradient of $\tilde{P}$ vanishes. … ►In this way, we associate a Riemann theta function with every compact Riemann surface $\mathrm{\Gamma }$. … ►Then the prime form on the corresponding compact Riemann surface $\mathrm{\Gamma }$ is defined by …

4: 8.27 Approximations

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Luke (1969b, p. 186) gives hypergeometric polynomial representations that converge uniformly on compact subsets of the $z$-plane that exclude $z=0$ and are valid for .

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5: Bibliography I

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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

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External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

Encodings:

BibTeX

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6: 21.9 Integrable Equations

… ►These parameters, including $𝛀$, are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition $u(x,y,0)$ (Deconinck and Segur (1998)). …

7: 24.11 Asymptotic Approximations

… ►uniformly for $x$ on compact subsets of $ℂ$. …

8: 28.11 Expansions in Series of Mathieu Functions

… ►The series (28.11.1) converges absolutely and uniformly on any compact subset of the strip $S$. …

9: 28.14 Fourier Series

… ►converge absolutely and uniformly on all compact sets in the $z$-plane. …

10: 1.16 Distributions

… ►If the support of $\varphi$ is a compact set (§1.9(vii)), then $\varphi$ is called a function of compact support. A test function is an infinitely differentiable function of compact support. ►A sequence $\{{\varphi }_n\}$ of test functions converges to a test function $\varphi$ if the support of every ${\varphi }_n$ is contained in a fixed compact set $K$ and as $n\to \mathrm{\infty }$ the sequence $\{{\varphi }_n^{(k)}\}$ converges uniformly on $K$ to ${\varphi }^{(k)}$ for $k=0,1,2,\mathrm{\dots }$. … ►, a function $f$ on $I$ which is absolutely Lebesgue integrable on every compact subset of $I$) such that …