plane

SearchAdvancedHelp

(0.000 seconds)

11—20 of 145 matching pages

11: 4.39 Continued Fractions

… ►where $z$ is in the open cut plane of Figure 4.37.1(i). …where $z$ is in the open cut plane of Figure 4.37.1(iii). …

12: 9.19 Approximations

… ►

§9.19(iii) Approximations in the Complex Plane

…

13: 19.38 Approximations

… ►They are valid over parts of the complex $k$ and $\varphi$ planes. …

14: 26.21 Tables

… ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts $\cancel{\equiv }\pm 2(mod5)$, partitions into parts $\cancel{\equiv }\pm 1(mod5)$, and unrestricted plane partitions up to 100. …

15: 4.25 Continued Fractions

… ►valid when $z$ lies in the open cut plane shown in Figure 4.23.1(i). …valid when $z$ lies in the open cut plane shown in Figure 4.23.1(ii). …valid when $z$ lies in the open cut plane shown in Figure 4.23.1(iv). …

16: 19.32 Conformal Map onto a Rectangle

… ►then $z(p)$ is a Schwartz–Christoffel mapping of the open upper-half $p$-plane onto the interior of the rectangle in the $z$-plane with vertices …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. …

17: 4.15 Graphics

… ►Figure 4.15.7 illustrates the conformal mapping of the strip onto the whole $w$-plane cut along the real axis from $-\mathrm{\infty }$ to $-1$ and $1$ to $\mathrm{\infty }$, where $w=\sin z$ and $z=\arcsin w$ (principal value). …Lines parallel to the real axis in the $z$-plane map onto ellipses in the $w$-plane with foci at $w=\pm 1$, and lines parallel to the imaginary axis in the $z$-plane map onto rectangular hyperbolas confocal with the ellipses. … ►

►

►

►►

(i) $z$-plane                                                  (ii) $w$-plane

… ►

Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify

…

18: 36.7 Zeros

… ►The zeros in Table 36.7.1 are points in the $𝐱=(x,y)$ plane, where $\mathrm{ph}{\mathrm{\Psi }}_2\left(𝐱\right)$ is undetermined. … ►Deep inside the bifurcation set, that is, inside the three-cusped astroid (36.4.10) and close to the part of the $z$-axis that is far from the origin, the zero contours form an array of rings close to the planes …The rings are almost circular (radii close to $(\Delta x)/9$ and varying by less than 1%), and almost flat (deviating from the planes $z_n$ by at most $(\Delta z)/36$). …In the symmetry planes (e. …There are also three sets of zero lines in the plane $z=0$ related by $2\pi /3$ rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates $(x=r\cos \theta ,y=r\sin \theta )$ is given by …

19: 1.9 Calculus of a Complex Variable

… ►Also, the union of $S$ and its limit points is the closure of $S$. … ► … ► … ►

Jordan Curve Theorem

… ►

§1.9(iv) Conformal Mapping

…

20: 4.29 Graphics

… ►The conformal mapping $w=\sinh z$ is obtainable from Figure 4.15.7 by rotating both the $w$-plane and the $z$-plane through an angle $\frac{1}{2}\pi$, compare (4.28.8). …