analyticity

(0.001 seconds)

21—30 of 146 matching pages

21: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
is a polynomial of degree $n$, and hence a solution of (31.2.1) that is analytic at all three finite singularities $0,1,a$. …
22: 3.8 Nonlinear Equations
§3.8 Nonlinear Equations
This is an iterative method for real twice-continuously differentiable, or complex analytic, functions: …
§3.8(v) Zeros of Analytic Functions
Newton’s rule is the most frequently used iterative process for accurate computation of real or complex zeros of analytic functions $f(z)$. …
23: 35.2 Laplace Transform
where the integration variable $\mathbf{X}$ ranges over the space ${\boldsymbol{\Omega}}$. … Then (35.2.1) converges absolutely on the region $\Re\left(\mathbf{Z}\right)>\mathbf{X}_{0}$, and $g(\mathbf{Z})$ is a complex analytic function of all elements $z_{j,k}$ of $\mathbf{Z}$. …
24: 3.12 Mathematical Constants
can be defined analytically in numerous ways, for example, …
27: 27.18 Methods of Computation: Primes
An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000). …
29: 32.2 Differential Equations
be a nonlinear second-order differential equation in which $F$ is a rational function of $w$ and $\ifrac{\mathrm{d}w}{\mathrm{d}z}$, and is locally analytic in $z$, that is, analytic except for isolated singularities in $\mathbb{C}$. … in which $a(z)$, $b(z)$, $c(z)$, $d(z)$, and $\phi(z)$ are locally analytic functions. …
30: 4.14 Definitions and Periodicity
4.14.7 $\cot z=\frac{\cos z}{\sin z}=\frac{1}{\tan z}.$