# compact

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## 1—10 of 30 matching pages

##### 1: 28.19 Expansions in Series of ${\mathrm{me}}_{\mathrm{\u012a\xbd}+2\u0101\x81\xa2n}$ Functions

##### 2: 18.24 Hahn Class: Asymptotic Approximations

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āŗWith $x=\mathrm{\u012a\xbb}\u0101\x81\xa2N$ and $\mathrm{\u012a\xbd}=n/N$, Li and Wong (2000) gives an asymptotic expansion for ${K}_{n}\u0101\x81\u201d(x;p,N)$ as $n\to \mathrm{\infty}$, that holds uniformly for $\mathrm{\u012a\xbb}$ and $\mathrm{\u012a\xbd}$ in compact subintervals of $(0,1)$.
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āŗThis expansion is uniformly valid in any compact
$x$-interval on the real line and is in terms of parabolic cylinder functions.
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##### 3: 21.7 Riemann Surfaces

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āŗIn almost all applications, a Riemann theta function is associated with a compact Riemann surface.
…Equation (21.7.1) determines a plane algebraic curve in ${\mathrm{\u0101\x84\x82}}^{2}$, 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 $\stackrel{~}{P}$ vanishes.
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*In this way, we associate a Riemann theta function with every compact Riemann surface $\mathrm{\u012a\x93}$.*… āŗThen the*prime form*on the corresponding compact Riemann surface $\mathrm{\u012a\x93}$ 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 $$.

##### 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 ${J}_{0}\u0101\x81\xa2(z)-i\u0101\x81\xa2{J}_{1}\u0101\x81\xa2(z)$ and of Bessel functions ${J}_{m}\u0101\x81\xa2(z)$ of any real order $m$
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Linear Algebra Appl. 194, pp. 35–70.
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##### 6: 21.9 Integrable Equations

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āŗThese parameters, including $\mathrm{\u0161\x9d\x9b\x80}$, are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition $u\u0101\x81\u201d(x,y,0)$ (Deconinck and Segur (1998)).
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##### 7: 24.11 Asymptotic Approximations

##### 8: 28.11 Expansions in Series of Mathieu Functions

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āŗThe series (28.11.1) converges absolutely and uniformly on any compact subset of the strip $S$.
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##### 9: 28.14 Fourier Series

##### 10: 1.16 Distributions

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āŗIf the support of $\mathrm{\u013b\x95}$ is a compact set (§1.9(vii)), then $\mathrm{\u013b\x95}$ is called a

*function of compact support*. A*test function*is an infinitely differentiable function of compact support. āŗA sequence $\{{\mathrm{\u013b\x95}}_{n}\}$ of test functions*converges*to a test function $\mathrm{\u013b\x95}$ if the support of every ${\mathrm{\u013b\x95}}_{n}$ is contained in a fixed compact set $K$ and as $n\to \mathrm{\infty}$ the sequence $\{{\mathrm{\u013b\x95}}_{n}^{(k)}\}$ converges uniformly on $K$ to ${\mathrm{\u013b\x95}}^{(k)}$ for $k=0,1,2,\mathrm{\dots}$. … āŗ, a function $f$ on $I$ which is absolutely Lebesgue integrable on every compact subset of $I$) such that …