# simply-connected

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## 2 matching pages

##### 1: 1.13 Differential Equations

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###### §1.13(i) Existence of Solutions

►A domain in the complex plane is*simply-connected*if it has no “holes”; more precisely, if its complement in the extended plane $\u2102\cup \{\mathrm{\infty}\}$ 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
$$A{w}_{1}(z)+B{w}_{2}(z)=0,$$
$\forall z\in D$,

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