# right-hand

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## 1—10 of 109 matching pages

##### 1: 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).

• ##### 2: 32.15 Orthogonal Polynomials
For this result and applications see Fokas et al. (1991): in this reference, on the right-hand side of Eq. …
##### 4: 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. …
##### 5: 24.19 Methods of Computation
If $\widetilde{N}_{2n}$ denotes the right-hand side of (24.19.1) but with the second product taken only for $p\leq\left\lfloor(\pi e)^{-1}2n\right\rfloor+1$, then $N_{2n}=\left\lceil\widetilde{N}_{2n}\right\rceil$ for $n\geq 2$. …
##### 6: 19.21 Connection Formulas
19.21.7 $(x-y)R_{D}\left(y,z,x\right)+(z-y)R_{D}\left(x,y,z\right)=3R_{F}\left(x,y,z% \right)-3y^{1/2}x^{-1/2}z^{-1/2},$
19.21.8 $R_{D}\left(y,z,x\right)+R_{D}\left(z,x,y\right)+R_{D}\left(x,y,z\right)=3x^{-1% /2}y^{-1/2}z^{-1/2},$
19.21.10 $2R_{G}\left(x,y,z\right)=zR_{F}\left(x,y,z\right)-\tfrac{1}{3}(x-z)(y-z)R_{D}% \left(x,y,z\right)+x^{1/2}y^{1/2}z^{-1/2},$ $z\neq 0$.
Because $R_{G}$ is completely symmetric, $x,y,z$ can be permuted on the right-hand side of (19.21.10) so that $(x-z)(y-z)\leq 0$ if the variables are real, thereby avoiding cancellations when $R_{G}$ is calculated from $R_{F}$ and $R_{D}$ (see §19.36(i)). …
##### 7: 19.25 Relations to Other Functions
19.25.7 $E\left(\phi,k\right)=2R_{G}\left(c-1,c-k^{2},c\right)-(c-1)R_{F}\left(c-1,c-k^% {2},c\right)-\ifrac{\sqrt{c-1}\sqrt{c-k^{2}}}{\sqrt{c}},$
All terms on the right-hand sides are nonnegative when $k^{2}\leq 0$, $0\leq k^{2}\leq 1$, or $1\leq k^{2}\leq c$, respectively. … The transformations in §19.7(ii) result from the symmetry and homogeneity of functions on the right-hand sides of (19.25.5), (19.25.7), and (19.25.14). … The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which $\wp\left(z\right)-e_{j}<0$, for some $j$. … The sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which $\sigma_{j}^{2}(z)<0$, for some $j$. …
##### 8: 16.10 Expansions in Series of ${{}_{p}F_{q}}$ Functions
When $|\zeta-1|<1$ the series on the right-hand side converges in the half-plane $\Re z<\frac{1}{2}$. …
##### 9: 1.6 Vectors and Vector-Valued Functions
where $\mathbf{n}$ is the unit vector normal to $\mathbf{a}$ and $\mathbf{b}$ whose direction is determined by the right-hand rule; see Figure 1.6.1.
##### 10: 1.8 Fourier Series
at every point at which $f(x)$ has both a left-hand derivative (that is, (1.4.4) applies when $h\to 0-$) and a right-hand derivative (that is, (1.4.4) applies when $h\to 0+$). … …