# 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: 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 $x\to\infty$
##### 6: 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 $(1,\infty)$. …
##### 9: 3.6 Linear Difference Equations
If, as $n\to\infty$, the wanted solution $w_{n}$ grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (backward) recursion is stable. … The least value of $N$ that satisfies (3.6.9) is found to be 16. … For a difference equation of order $k$ ($\geq 3$), …Typically $k-\ell$ conditions are prescribed at the beginning of the range, and $\ell$ conditions at the end. …
##### 10: 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 $z=\infty$. …