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[[Category:Approximations and expansions]]

Please remove this comment and the {{TEX|auto}} line below, ...commonly employed; the corresponding asymptotic expansions are asymptotic expansions in the sense of Poincaré.

...diaofmath.org/legacyimages/e/e035/e035060/e0350606.png" /> are independent and identically distributed), is the density of the standard [[Normal distribution|normal distribution]], and

Please remove this comment and the {{TEX|auto}} line below, plane, and the functions $ f( z) $

Please remove this comment and the {{TEX|auto}} line below, ...totic approximations of solutions of problems in the theory of diffraction and propagation of waves. The ray method consists of an aggregate of methods of

Please remove this comment and the {{TEX|auto}} line below, is complex, and $ f, S \in C ^ \infty ( \mathbf R ^ {n} ) $.

Please remove this comment and the {{TEX|auto}} line below, and finite positive variance $ \sigma ^ {2} $.

...ctorial to a [[Meromorphic function|meromorphic function]] on $\mathbb C$) and $z^\nu$ is given by ${\rm exp}\, (\log z)$, with the convention of having c The series on the right-hand side of \eqref{e:Bessel_f} converges absolutely and uniformly on any compact subset of $\mathbb C$. The functions $J_\nu$ are

Please remove this comment and the {{TEX|auto}} line below, and $ Y _ {1} \dots Y _ {m} $

Please remove this comment and the {{TEX|auto}} line below, Weak convergence or convergence in variation, and defined as follows. A sequence of distributions (probability measures) $

Please remove this comment and the {{TEX|auto}} line below, ...a difference in the numbers of boundary conditions for the initial problem and the degenerate one (with the small parameter taking the value zero), as wel

...uthor(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike Lic ...a binomial random variable $T$ with distribution $B(n,p)$, with mean $np$ and variance $npq (q=1-p)$, the normal approximation is given , for integers $0

Please remove this comment and the {{TEX|auto}} line below, and finite variances $ {\mathsf D} X _ {k} = b _ {k} $,

Please remove this comment and the {{TEX|auto}} line below, ...tered turbulent flows are theoretically described with the aid of partial, and mostly semi-empirical, models that are applicable to rather narrow types of

Please remove this comment and the {{TEX|auto}} line below, ...ous problems employed in many branches of mathematics, mechanics, physics, and technology. In this article the principal ideas of perturbation theory are

...Riemann's zeta-function, its generalizations and analogues. Zeta-functions and their generalizations in the form of $L$-functions (cf. [[Dirichlet L-funct which converges absolutely and uniformly in any bounded domain of the complex $s$-plane for which $\sigma\