# in a domain

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## 1—10 of 42 matching pages

##### 1: Bibliography Y
• A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1985) The calculation of the Riemann zeta function in the complex domain. USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.
• A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1988) Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.
• ##### 2: 3.7 Ordinary Differential Equations
where $f$, $g$, and $h$ are analytic functions in a domain $D\subset\mathbb{C}$. … Assume that we wish to integrate (3.7.1) along a finite path $\mathscr{P}$ from $z=a$ to $z=b$ in a domain $D$. …
##### 3: 1.10 Functions of a Complex Variable
Let $f_{1}(z)$ be analytic in a domain $D_{1}$. … Suppose the subarc $z(t)$, $t\in[t_{j-1},t_{j}]$ is contained in a domain $D_{j}$, $j=1,\dots,n$. … If $f(z)$ is analytic in a domain $D$, $z_{0}\in D$ and $\left|f(z)\right|\leq\left|f(z_{0})\right|$ for all $z\in D$, then $f(z)$ is a constant in $D$. … Assume that for each $t\in[a,b]$, $f(z,t)$ is an analytic function of $z$ in $D$, and also that $f(z,t)$ is a continuous function of both variables. … Suppose $a_{n}=a_{n}(z)$, $z\in D$, a domain. …
##### 4: 1.9 Calculus of a Complex Variable
A domain $D$, say, is an open set in $\mathbb{C}$ that is connected, that is, any two points can be joined by a polygonal arc (a finite chain of straight-line segments) lying in the set. … A function $f(z)$ is analytic in a domain $D$ if it is analytic at each point of $D$. … … Suppose $f(z)$ is analytic in a domain $D$ and $C_{1},C_{2}$ are two arcs in $D$ passing through $z_{0}$. … Suppose the series $\sum^{\infty}_{n=0}f_{n}(z)$, where $f_{n}(z)$ is continuous, converges uniformly on every compact set of a domain $D$, that is, every closed and bounded set in $D$. …
##### 5: 1.13 Differential Equations
A domain in the complex plane is simply-connected if it has no “holes”; more precisely, if its complement in the extended plane $\mathbb{C}\cup\{\infty\}$ is connected. … where $z\in D$, a simply-connected domain, and $f(z)$, $g(z)$ are analytic in $D$, has an infinite number of analytic solutions in $D$. …
1.13.6 $Aw_{1}(z)+Bw_{2}(z)=0,$ $\forall z\in D$,
##### 6: Bibliography W
• R. Wong and Y. Zhao (2004) Uniform asymptotic expansion of the Jacobi polynomials in a complex domain. Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.
• ##### 7: Bibliography K
• A. A. Kapaev and A. V. Kitaev (1993) Connection formulae for the first Painlevé transcendent in the complex domain. Lett. Math. Phys. 27 (4), pp. 243–252.
• M. K. Kerimov and S. L. Skorokhodov (1984a) Calculation of modified Bessel functions in a complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.
• ##### 8: 3.10 Continued Fractions
However, other continued fractions with the same limit may converge in a much larger domain of the complex plane than the fraction given by (3.10.4) and (3.10.5). …
##### 9: 3.3 Interpolation
If $f$ is analytic in a simply-connected domain $D$1.13(i)), then for $z\in D$, … If $f$ is analytic in a simply-connected domain $D$, then for $z\in{D}$, …
##### 10: Bibliography H
• Y. P. Hsu (1993) Development of a Gaussian hypergeometric function code in complex domains. Internat. J. Modern Phys. C 4 (4), pp. 805–840.