punctured%20neighborhood

(0.001 seconds)

21—30 of 125 matching pages

21: William P. Reinhardt

… ►

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

Zhang and Jin (1996, pp. 652, 689) includes $\operatorname{Si}\left(x\right)$ , $\operatorname{Ci}\left(x\right)$ , $x=0(.5)20(2)30$ , 8D; $\operatorname{Ei}\left(x\right)$ , $E_{1}\left(x\right)$ , $x=[0,100]$ , 8S.

… ►

•

Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $ze^{z}E_{1}\left(z\right)$ , $x=-19(1)20$ , $y=0(1)20$ , 6D; $e^{z}E_{1}\left(z\right)$ , $x=-4(.5)-2$ , $y=0(.2)1$ , 6D; $E_{1}\left(z\right)+\ln z$ , $x=-2(.5)2.5$ , $y=0(.2)1$ , 6D.

►

•

Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $E_{1}\left(z\right)$ , $\pm x=0.5,1,3,5,10,15,20,50,100$ , $y=0(.5)1(1)5(5)30,50,100$ , 8S.

23: Peter L. Walker

… ►

20 Theta Functions

…

24: Staff

… ►

William P. Reinhardt, University of Washington, Chaps. 20, 22, 23

… ►

Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23

… ►

William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23

… ►

Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23

…

25: 1.9 Calculus of a Complex Variable

… ►

Point Sets in $\mathbb{C}$

… ►An open set in

\mathbb{C}

is one in which each point has a neighborhood that is contained in the set. … ►A system of open disks around infinity is given by …Each

S_{r}

is a neighborhood of

\infty

. Also, …

26: 2.11 Remainder Terms; Stokes Phenomenon

… ►In effect, (2.11.7) “corrects” (2.11.6) by introducing a term that is relatively exponentially small in the neighborhood of

\operatorname{ph}z=\pi

, is increasingly significant as

\operatorname{ph}z

passes from

\pi

\frac{3}{2}\pi

, and becomes the dominant contribution after

\operatorname{ph}z

passes

\frac{3}{2}\pi

. … ►For example, using double precision

d_{20}

is found to agree with (2.11.31) to 13D. …

27: 24.20 Tables

… ►Wagstaff (1978) gives complete prime factorizations of

N_{n}

and

E_{n}

for

n=20(2)60

and

n=8(2)42

, respectively. …

28: 6.20 Approximations

… ►

•

Cody and Thacher (1968) provides minimax rational approximations for $E_{1}\left(x\right)$ , with accuracies up to 20S.

►

•

Cody and Thacher (1969) provides minimax rational approximations for $\operatorname{Ei}\left(x\right)$ , with accuracies up to 20S.

►

•

MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions $\mathrm{f}$ and $\mathrm{g}$ , with accuracies up to 20S.

…

29: Foreword

… ►November 20, 2009 …

30: 13.30 Tables

… ►

•

Zhang and Jin (1996, pp. 411–423) tabulates $M\left(a,b,x\right)$ and $U\left(a,b,x\right)$ for $a=-5(.5)5$ , $b=0.5(.5)5$ , and $x=0.1,1,5,10,20,30$ , 8S (for $M\left(a,b,x\right)$ ) and 7S (for $U\left(a,b,x\right)$ ).

…