Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1167.33002
Elbert, Árpád; Laforgia, Andrea
The zeros of the complementary error function. (English)
[J] Numer. Algorithms 49, No. 1-4, 153-157 (2008). ISSN 1017-1398; ISSN 1572-9265/e

The well-known complementary error function erfc ($z$) is defined by $$\text{erfc (z)}=\frac{2}{\sqrt{\pi}}\int_z^\infty e^{-s^2}ds.$$ It is shown that erfc ($z$) has no zeros in the sector $3\pi/4\leq\arg\,z\leq 5\pi/4$. \par The authors establish this result by consideration of the two sectors $3\pi/4\leq\arg\,z\leq\pi$ and $\pi<\arg\,z\leq 5\pi/4$. In the first sector, they write $z=-X+iY$, with $X\geq 0$ and $0\leq Y\leq X$, and decompose the integral into integrals taken along the straight line paths $(z,-X)$, $(-X,0)$ and $(0,\infty)$. They show that the real part of the decomposed integral is positive. Similar considerations with $z=-X-iY$ are applied to the second sector.
[R. B. Paris (Dundee)]

MSC 2000:: *33B20 Incomplete beta and gamma functions

Keywords: zeros; complementary error function

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]