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1: 28.19 Expansions in Series of me Ī½ + 2 ā¢ n Functions
ā–ŗThe series (28.19.2) converges absolutely and uniformly on compact subsets within S . …
2: 18.24 Hahn Class: Asymptotic Approximations
ā–ŗWith x = Ī» ā¢ N and Ī½ = n / N , Li and Wong (2000) gives an asymptotic expansion for K n ā” ( x ; p , N ) as n , that holds uniformly for Ī» and Ī½ in compact subintervals of ( 0 , 1 ) . … ā–ŗThis 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
ā–ŗIn almost all applications, a Riemann theta function is associated with a compact Riemann surface. …Equation (21.7.1) determines a plane algebraic curve in ā„‚ 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 P ~ vanishes. … ā–ŗIn this way, we associate a Riemann theta function with every compact Riemann surface Ī“ .ā–ŗThen the prime form on the corresponding compact Riemann surface Ī“ is defined by …
4: 8.27 Approximations
  • 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 | ph ā” z | < Ļ€ .

  • 5: Bibliography I
  • Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi, and M. Harada (1993) The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J 0 ā¢ ( z ) i ā¢ J 1 ā¢ ( z ) and of Bessel functions J m ā¢ ( z ) of any real order m . Linear Algebra Appl. 194, pp. 35–70.
  • 6: 21.9 Integrable Equations
    ā–ŗThese parameters, including š›€ , are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition u ā” ( x , y , 0 ) (Deconinck and Segur (1998)). …
    7: 24.11 Asymptotic Approximations
    ā–ŗuniformly for x on compact subsets of ā„‚ . …
    8: 28.11 Expansions in Series of Mathieu Functions
    ā–ŗThe series (28.11.1) converges absolutely and uniformly on any compact subset of the strip S . …
    9: 28.14 Fourier Series
    ā–ŗconverge absolutely and uniformly on all compact sets in the z -plane. …
    10: 1.16 Distributions
    ā–ŗIf the support of Ļ• is a compact set (§1.9(vii)), then Ļ• is called a function of compact support. A test function is an infinitely differentiable function of compact support. ā–ŗA sequence { Ļ• n } of test functions converges to a test function Ļ• if the support of every Ļ• n is contained in a fixed compact set K and as n the sequence { Ļ• n ( k ) } converges uniformly on K to Ļ• ( k ) for k = 0 , 1 , 2 , . … ā–ŗ, a function f on I which is absolutely Lebesgue integrable on every compact subset of I ) such that …