limiting values

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1: 4.31 Special Values and Limits

§4.31 Special Values and Limits

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2: 6.16 Mathematical Applications

… ►Hence if $x=\pi /(2n)$ and $n\to \mathrm{\infty }$, 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 $\mu \in \mathbb{Z}$. …

4: 22.5 Special Values

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§22.5(ii) Limiting Values of $k$

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5: 19.6 Special Cases

§19.6 Special Cases

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§19.6(v) $R_C(x,y)$

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6: 4.17 Special Values and Limits

§4.17 Special Values and Limits

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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 $\zeta$. …