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searching for Radius of convergence 30 found (117 total)

Analytic continuation (3,929 words) [view diff] exact match in snippet view article find links to article

_{k=0}^{\infty }(-1)^{k}(z-1)^{k}.} By the Cauchy–Hadamard theorem, its radius of convergence is 1. That is, f {\displaystyle f} is defined and analytic on the

Principal part (283 words) [view diff] exact match in snippet view article find links to article

f} at a {\displaystyle a} . If the Laurent series has an inner radius of convergence of 0 {\displaystyle 0} , then f ( z ) {\displaystyle f(z)} has an

Laurent series (2,673 words) [view diff] exact match in snippet view article find links to article

sum (meaning it has infinitely many non-zero terms). If the inner radius of convergence of the Laurent series for f {\displaystyle f} is 0, then f {\displaystyle

Fuchs's theorem (258 words) [view diff] exact match in snippet view article find links to article

positive real r, where y0 is a solution of the first kind. Its radius of convergence is at least as large as the minimum of the radii of convergence

Convolution power (1,136 words) [view diff] exact match in snippet view article find links to article

absolutely in norm provided that the norm of x is less than the radius of convergence of the original series defining F(z). In particular, it is possible

Alonzo King LINES Ballet (992 words) [view diff] case mismatch in snippet view article find links to article

Field 2009: Scheherazade, Refraction, & Dust and Light 2008: The Radius of Convergence, The Steady Articulation of Perseverance 2007: Rasa, Irregular Pearl

The Solitude of Prime Numbers (soundtrack) (152 words) [view diff] case mismatch in snippet view article

"Cicatrix" 2:02 13. "Abscissa" 1:41 17. "Isolated Primes" 1:42 19. "Radius of Convergence" 4:24 23. "Separatrix" 1:00 29. "The Snow Angel" 1:42 31. "Apnoea"

Kepler's equation (3,614 words) [view diff] exact match in snippet view article find links to article

infinity at these values of M {\displaystyle M} . This means that the radius of convergence of the Maclaurin series is cosh − 1 ⁡ ( 1 / e ) − 1 − e 2 {\displaystyle

Conformal bootstrap (791 words) [view diff] exact match in snippet view article find links to article

turning the product into an algebra); the sum must have a non-zero radius of convergence. This leads to decompositions of correlation functions into structure

Formal calculation (836 words) [view diff] exact match in snippet view article find links to article

a function by taking numerical values for the variable within a radius of convergence. In a formal power series, the powers of the variable are used only

Legendre's formula (1,036 words) [view diff] exact match in snippet view article find links to article

from Legendre's formula that the p-adic exponential function has radius of convergence p − 1 / ( p − 1 ) {\displaystyle p^{-1/(p-1)}} . Legendre, A. M

Infinite-dimensional holomorphy (1,358 words) [view diff] exact match in snippet view article find links to article

holomorphic functions defined on the entire space which have a finite radius of convergence.[1] In general, given two complex topological vector spaces X and

Alfred Pringsheim (3,098 words) [view diff] exact match in snippet view article find links to article

Borel, states that a power series with positive coefficients and radius of convergence equal to 1 has necessarily a singularity at the point 1. This theorem

Function of several complex variables (17,693 words) [view diff] exact match in snippet view article find links to article

. In this way it is possible to have a similar, combination of radius of convergence for a one complex variable. This combination is generally not unique

Resurgent function (743 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \psi (t)=\phi (1/t)\in \mathbb {C} [[t]]} has a positive radius of convergence. C { z − 1 } {\displaystyle \mathbb {C} \{z^{-1}\}} denotes the

Alonzo King (900 words) [view diff] case mismatch in snippet view article find links to article

Field 2009: Scheherazade, Refraction, Dust and Light 2008: The Radius of Convergence, The Steady Articulation of Perseverance 2007: Rasa, Irregular Pearl

Divergent series (5,040 words) [view diff] exact match in snippet view article find links to article

around zero, and hence has a Maclaurin series G(z) with a positive radius of convergence, then L(G(z)) = g(z) in the Mittag-Leffler star. Moreover, convergence

Perturbation theory (2,959 words) [view diff] exact match in snippet view article find links to article

ε {\displaystyle \ \varepsilon \ } converges with a nonzero radius of convergence, the perturbation problem is called a regular perturbation problem

Taylor's theorem (9,679 words) [view diff] exact match in snippet view article find links to article

1}(x-a)+c_{2}(x-a)^{2}+\cdots ,\qquad |x-a|<r.} In general, the radius of convergence of a power series can be computed from the Cauchy–Hadamard formula

Analytic function of a matrix (2,213 words) [view diff] exact match in snippet view article find links to article

beyond the set of matrices with spectral radius smaller than the radius of convergence of the power series. Note that there is also a connection to divided

General Dirichlet series (1,999 words) [view diff] exact match in snippet view article find links to article

These formulas are similar to the Cauchy–Hadamard theorem for the radius of convergence of a power series. If ∑ a k {\displaystyle \sum a_{k}} is divergent

Conformal field theory (7,049 words) [view diff] exact match in snippet view article find links to article

because in conformal field theory, the operator product expansion's radius of convergence is finite (i.e. it is not zero). Provided the positions x 1 , x

Poisson boundary (2,317 words) [view diff] exact match in snippet view article find links to article

y)=\sum _{n\geq 1}p_{n}(x,y)r^{n}.} Denote by R {\displaystyle R} the radius of convergence of this power series and define for 1 ≤ r ≤ R {\displaystyle 1\leq

Holomorphic functional calculus (5,483 words) [view diff] exact match in snippet view article find links to article

From above it is evident that all that is really needed is the radius of convergence of the MacLaurin series be greater than ǁTǁ, the operator norm of

Incomplete gamma function (7,107 words) [view diff] exact match in snippet view article find links to article

{z^{2}}{(s+1)(s+2)}}+{\frac {z^{3}}{(s+1)(s+2)(s+3)}}+\cdots } has an infinite radius of convergence. Again with confluent hypergeometric functions and employing Kummer's

Leibniz integral rule (11,304 words) [view diff] exact match in snippet view article find links to article

application is the fact that power series are differentiable in their radius of convergence.[citation needed] The Leibniz integral rule is used in the derivation

Boltzmann sampler (2,934 words) [view diff] exact match in snippet view article find links to article

generating function C ( z ) {\displaystyle C(z)} which has a nonzero radius of convergence ρ {\displaystyle \rho } , i.e. is complex analytic. Formally speaking

Beta distribution (40,689 words) [view diff] exact match in snippet view article find links to article

⋅ ) {\displaystyle M_{X}(\alpha ;\beta ;\cdot )} has a positive radius of convergence,[citation needed] the beta distribution is determined by its moments

Coherent states in mathematical physics (5,756 words) [view diff] exact match in snippet view article find links to article

open disc in the complex plane of radius L {\displaystyle L} , the radius of convergence of the series ∑ n = 0 ∞ α n ε n ! {\textstyle \sum _{n=0}^{\infty

Lemniscate elliptic functions (23,974 words) [view diff] exact match in snippet view article find links to article

of sl {\displaystyle \operatorname {sl} } which has only finite radius of convergence (because it is not entire). We define S {\displaystyle S} and T