zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The zeros of the complementary error function. (English) Zbl 1167.33002

The well-known complementary error function erfc (z) is defined by

erfc(z)=2 π z e -s 2 ds·

It is shown that erfc (z) has no zeros in the sector 3π/4argz5π/4.

The authors establish this result by consideration of the two sectors 3π/4argzπ and π<argz5π/4. In the first sector, they write z=-X+iY, with X0 and 0YX, and decompose the integral into integrals taken along the straight line paths (z,-X), (-X,0) and (0,). They show that the real part of the decomposed integral is positive. Similar considerations with z=-X-iY are applied to the second sector.

MSC:
33B20Incomplete beta and gamma functions
References:
[1]Tricomi, F.G.: Funzioni ipergeometriche confluenti. Consiglio Nazionale delle Ricerche, Monografie Matematiche, 1, Edizioni Cremonese, Roma (1954)