# limiting values

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## 1—10 of 88 matching pages

##### 2: 6.16 Mathematical Applications
Hence if $x=\pi/(2n)$ and $n\to\infty$, then the limiting value of $S_{n}(x)$ overshoots $\frac{1}{4}\pi$ by approximately 18%. Similarly if $x=\pi/n$, then the limiting value of $S_{n}(x)$ undershoots $\frac{1}{4}\pi$ by approximately 10%, and so on. …
##### 3: 14.24 Analytic Continuation
the limiting value being taken in (14.24.1) when $2\nu$ is an odd integer. … the limiting value being taken in (14.24.4) when $\mu\in\mathbb{Z}$. …
##### 7: 10.72 Mathematical Applications
In regions in which the function $f(z)$ has a simple pole at $z=z_{0}$ and $(z-z_{0})^{2}g(z)$ is analytic at $z=z_{0}$ (the case $\lambda=-1$ in §10.72(i)), asymptotic expansions of the solutions $w$ of (10.72.1) for large $u$ can be constructed in terms of Bessel functions and modified Bessel functions of order $\pm\sqrt{1+4\rho}$, where $\rho$ is the limiting value of $(z-z_{0})^{2}g(z)$ as $z\to z_{0}$. …
##### 8: 8.14 Integrals
In (8.14.1) and (8.14.2) limiting values are used when $b=0$. …
##### 9: 10.34 Analytic Continuation
If $\nu=n(\in\mathbb{Z})$, then limiting values are taken in (10.34.2) and (10.34.4): …
##### 10: 31.9 Orthogonality
The right-hand side may be evaluated at any convenient value, or limiting value, of $\zeta$ in $(0,1)$ since it is independent of $\zeta$. …