# values at infinity

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##### 3: 6.4 Analytic Continuation
Analytic continuation of the principal value of $E_{1}\left(z\right)$ yields a multi-valued function with branch points at $z=0$ and $z=\infty$. …
##### 5: 10.9 Integral Representations
Also, $(t^{2}-1)^{\nu-\frac{1}{2}}$ is continuous on the path, and takes its principal value at the intersection with the interval $(1,\infty)$. …
##### 6: 12.14 The Function $W\left(a,x\right)$
$W\left(a,x\right)$ and $W\left(a,-x\right)$ form a numerically satisfactory pair of solutions when $-\infty.
###### §12.14(ii) Valuesat$z=0$ and Wronskian
These follow from the contour integrals of §12.5(ii), which are valid for general complex values of the argument $z$ and parameter $a$. … Then as $x\to\infty$
##### 7: 13.14 Definitions and Basic Properties
In general $M_{\kappa,\mu}\left(z\right)$ and $W_{\kappa,\mu}\left(z\right)$ are many-valued functions of $z$ with branch points at $z=0$ and $z=\infty$. …
##### 8: 4.13 Lambert $W$-Function
$W_{0}\left(z\right)$ is a single-valued analytic function on $\mathbb{C}\setminus(-\infty,-{\mathrm{e}}^{-1}]$, real-valued when $z>-{\mathrm{e}}^{-1}$, and has a square root branch point at $z=-{\mathrm{e}}^{-1}$. …The other branches $W_{k}\left(z\right)$ are single-valued analytic functions on $\mathbb{C}\setminus(-\infty,0]$, have a logarithmic branch point at $z=0$, and, in the case $k=\pm 1$, have a square root branch point at $z=-{\mathrm{e}}^{-1}\mp 0\mathrm{i}$ respectively. …
##### 9: 1.4 Calculus of One Variable
For the functions discussed in the following DLMF chapters these two integration measures are adequate, as these special functions are analytic functions of their variables, and thus $C^{\infty}$, and well defined for all values of these variables; possible exceptions being at boundary points. …