...the symbols $o$, $O$ or the equivalence sign $\sim$ ([[Asymptotic equality|asymptotic equality]] of functions).
Examples of asymptotic formulas:
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...is a function defined on $M$, then $\{\psi(x)\phi_n(x)\}$ will also be an asymptotic sequence.
Examples of asymptotic sequences:
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$#C+1 = 20 : ~/encyclopedia/old_files/data/A013/A.0103670 Asymptotic expansion
is some given [[asymptotic sequence]] as $ x \rightarrow x _ {0} $.
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An asymptotic representation which provides approximate values of the
where $\abs{\theta(n)} < 1/12n$. The asymptotic equalities
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may have different asymptotic expressions when $ | z | \rightarrow \infty $
has the following asymptotic expansion when $ | z | \rightarrow \infty $:
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$#C+1 = 31 : ~/encyclopedia/old_files/data/A013/A.0103750 Asymptotic power series
An asymptotic series with respect to the sequence
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''of asymptotic estimation''
A method for determining the asymptotic behaviour as $ 0 < \lambda \rightarrow + \infty $
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...the limits of the class of linear estimators. For example, the statistical analysis of a linear regression model (see [[Linear regression|Linear regression]])
...)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> H. Scheffé, "Analysis of variance" , Wiley (1959)</TD></TR></table>
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...an important role in various problems of physics, mechanics and asymptotic analysis, its solutions are regarded as forming a distinct class of special function
...5.35002}} (In Russian) (Translation: "Short-Wavelength Diffraction Theory. Asymptotic Methods", Springer, 1991 {{ZBL|0742.35002}})
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...ernate and the series is enveloping in the strict sense. This series is an asymptotic expansion for $f(x)$ as $x\to+\infty$; if it is divergent, then it is calle
...</TD> <TD valign="top"> G. Pólya, G. Szegö, "Problems and theorems in analysis" , Springer (1976) pp. Chapts. 1–2 (Translated from German)</TD></TR><
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A method for computing the asymptotic expansion of integrals of the form
...otic expansions of integrals of the form (*). It can be used to derive the asymptotic expansions for Laplace, Fourier and Mellin transforms, as well as for trans
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...$f$ holomorphic in $S$, for which the formal series $\sum c_k z^k$ is an [[asymptotic series]]:
...gin and admitting an asymptotic series, is necessarily holomorphic, so its asymptotic series must converge.
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cf. [[Spectral analysis of a stationary stochastic process|Spectral analysis of a stationary stochastic process]]). The regression spectrum for $ M (
...ectrum can be used to express a necessary and sufficient condition for the asymptotic efficiency of an estimator for $ \beta $
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...es quantiles of successive subsets [[#References|[a4]]], in which case the asymptotic distribution is determined by recursive application of polynomials. A tree-
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with radius of convergence 1 satisfies on the real axis the asymptotic equality
satisfy the asymptotic equality
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...escribed in [[#References|[a6]]], which presents a unified approach to the analysis of data resulting from an experiment involving multinomial populations. Thu
have to be estimated. He has given results concerning the asymptotic variance-covariance matrix of the estimators.
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have the same distribution. Asymptotic tests can be based on the following theorem: If $ \min ( m , n ) \rightar
...stribution function (cf. [[Statistical estimator|Statistical estimator]]). Asymptotic expansions for the distribution functions of the statistics $ D _ {m,n}
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...oportion of numbers less than $X$ which are not arithmetic is [[Asymptotic analysis|asymptotically]] {{cite|Bateman et al (1981)}}
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4) Asymptotic methods of investigation of loss systems may also be effective for the stud
...s with a large number of channels is conducted both by means of asymptotic analysis of explicit formulas, which become effective for large $ n $,
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...amplitude. In order to calculate the oscillation process more accurately, asymptotic methods are employed. As $ \mu $
...n]] with period $ 1.614 \mu $ (to a first approximation). More accurate asymptotic expansions of magnitudes characterizing relaxation oscillations [[#Referenc
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