asymptotic series in a sentence
1) In fact, asymptotic series are the norm.
2) Stokes' research on asymptotic series led to fundamental insights about such series.
3) They reappeared in 1886 with Poincaré's work on asymptotic series .
4) What it actually plots are the Taylor's series and the asymptotic series simultaneously.
asymptotic series example sentences5) He received his doctorate of science in 1886 for a thesis on asymptotic series .
6) Watson's theorem gives conditions for a function to be the Borel sum of its asymptotic series .
7) Even for analytic functions, the series on the right is not guaranteed to converge; it may be an asymptotic series . However, it can be used to obtain more accurate approximations for the derivative.
8) Carleman's theorem shows that a function is uniquely determined by an asymptotic series in a sector provided the errors in the finite order approximations do not grow too fast.
9) This is then a divergent or asymptotic series, or it can be interpreted as a symbolic shorthand for a differential equation that the sum satisfies.
10) After a certain order __FORMULA__ however, the results become increasingly worse since the series are usually divergent (being asymptotic series ).
11) These corrections, being'small' compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series .
12) In 1918, Hardy and Ramanujan studied the partition function "P"("n") extensively and gave a non-convergent asymptotic series that permits exact computation of the number of partitions of an integer.
13) Because the theory is'sick' for any negative value of the coupling constant, the series do not converge, but are an asymptotic series .
14) The values Φ("x") may be approximated very accurately by a variety of methods, such as numerical integration, Taylor series, asymptotic series and continued fractions.
example sentences with asymptotic15) In fact, after a certain number of terms, a typical asymptotic series reaches its best approximation; if more terms are included, most such series will produce worse answers.
16) The difference is that an asymptotic series cannot be made to produce an answer as exact as desired, the way that convergent series can.
17) asymptotic series, otherwise asymptotic expansions, are infinite series whose partial sums become good approximations in the limit of some point of the domain.
18) Including more terms from the zeta series yields a better approximation, as does factoring in the asymptotic series in Stirling's approximation.
19) By convention, the asymptotic series is written as:
20) __FORMULA__ as an asymptotic series where __FORMULA__ and __FORMULA__.
21) " In mathematical analysis, asymptotic series are one of the most popular tools employed to approach such questions.
22) For |"z"| ≫ 1, the polylogarithm can be expanded into asymptotic series in terms of ln(−"z"):
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