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##### 1: 5.21 Methods of Computation
An effective way of computing $\Gamma\left(z\right)$ in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3). …
##### 4: 25.19 Tables
• Abramowitz and Stegun (1964) tabulates: $\zeta\left(n\right)$, $n=2,3,4,\dots$, 20D (p. 811); $\operatorname{Li}_{2}\left(1-x\right)$, $x=0(.01)0.5$, 9D (p. 1005); $f(\theta)$, $\theta=15^{\circ}(1^{\circ})30^{\circ}(2^{\circ})90^{\circ}(5^{\circ})180^{\circ}$, $f(\theta)+\theta\ln\theta$, $\theta=0(1^{\circ})15^{\circ}$, 6D (p. 1006). Here $f(\theta)$ denotes Clausen’s integral, given by the right-hand side of (25.12.9).

• ##### 5: 32.15 Orthogonal Polynomials
For this result and applications see Fokas et al. (1991): in this reference, on the right-hand side of Eq. …
##### 6: 16.5 Integral Representations and Integrals
In the case $p=q$ the left-hand side of (16.5.1) is an entire function, and the right-hand side supplies an integral representation valid when $|\operatorname{ph}\left(-z\right)|<\pi/2$. In the case $p=q+1$ the right-hand side of (16.5.1) supplies the analytic continuation of the left-hand side from the open unit disk to the sector $|\operatorname{ph}\left(1-z\right)|<\pi$; compare §16.2(iii). Lastly, when $p>q+1$ the right-hand side of (16.5.1) can be regarded as the definition of the (customarily undefined) left-hand side. In this event, the formal power-series expansion of the left-hand side (obtained from (16.2.1)) is the asymptotic expansion of the right-hand side as $z\to 0$ in the sector $|\operatorname{ph}\left(-z\right)|\leq(p+1-q-\delta)\pi/2$, where $\delta$ is an arbitrary small positive constant. …
##### 8: 2.3 Integrals of a Real Variable
assume $a$ and $b$ are finite, and $q(t)$ is infinitely differentiable on $[a,b]$. … When $p(t)$ is real and $x$ is a large positive parameter, the main contribution to the integral When the parameter $x$ is large the contributions from the real and imaginary parts of the integrand in
##### 9: 2.4 Contour Integrals
Let $\mathscr{P}$ denote the path for the contour integral
2.4.14 $I(z)=\int_{t_{0}}^{b}e^{-zp(t)}q(t)\,\mathrm{d}t-\int_{t_{0}}^{a}e^{-zp(t)}q(t% )\,\mathrm{d}t,$
and apply the result of §2.4(iii) to each integral on the right-hand side, the role of the series (2.4.11) being played by the Taylor series of $p(t)$ and $q(t)$ at $t=t_{0}$. …Thus the right-hand side of (2.4.14) reduces to the error terms. …
##### 10: 19.32 Conformal Map onto a Rectangle
As $p$ proceeds along the entire real axis with the upper half-plane on the right, $z$ describes the rectangle in the clockwise direction; hence $z(x_{3})$ is negative imaginary. …