asymptotic power series

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• Asymptotic theory — is the branch of mathematics which studies properties of asymptotic expansions.The most known result of this field is the prime number theorem:Let pi;( x ) be the number of prime numbers that are smaller than or equal to x .The limit:lim {x… …   Wikipedia

• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

• Asymptotic expansion — In mathematics an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a …   Wikipedia

• Power law — A power law is any polynomial relationship that exhibits the property of scale invariance. The most common power laws relate two variables and have the form:f(x) = ax^k! +o(x^k),where a and k are constants, and o(x^k) is of x. Here, k is… …   Wikipedia

• Asymptotic analysis — This article is about the comparison of functions as inputs approach infinite. For asymptotes in geometry, see asymptotic curve. In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has… …   Wikipedia

• Series acceleration — In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve… …   Wikipedia

• Divergent series — In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit. If a series converges, the individual terms of the series must approach… …   Wikipedia

• Binomial series — In mathematics, the binomial series is the Taylor series at x = 0 of the function f given by f(x) = (1 + x) α, where α ∈ C is an arbitrary complex number. Explicitly, and the binomial series is the power series… …   Wikipedia

• Summation of Grandi's series — General considerationstability and linearityThe formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: *Adding or subtracting two series term by term, *Multiplying through by a scalar term by term, *… …   Wikipedia

• Method of matched asymptotic expansions — In mathematics, particularly in solving singularly perturbed differential equations, the method of matched asymptotic expansions is a common approach to finding an accurate approximation to a problem s solution. Contents 1 Method overview 2… …   Wikipedia

• Generating function — This article is about generating functions in mathematics. For generating functions in classical mechanics, see Generating function (physics). For signalling molecule, see Epidermal growth factor. In mathematics, a generating function is a formal …   Wikipedia