zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Asymptotics and bounds of the roots of equations. Ed. by L. Eh. Rejzin’. ({\cyr Asimptotika i otsenki korneĭ uravneniĭ}.) (Russian) Zbl 0731.65034
Riga: Zinatne. 344 p. R. 4.20 (1991).
The book consists of an introduction and four chapters. Chapter one is a review of some methods and theorems which are used in the numerical treatment of equations of the type $F(x)=0$, $F: \Bbb R\to \Bbb R$ and can be realized in a very general way (with the help of analytical expression, integral, differential equation or whatever). Among these methods are both well known ones and those which can be found only in very special articles (as the usage of integral representations -- for example). Chapter two is devoted to the study of quasipolynomials and the behaviour of their roots -- asymptotics of roots, asymptotic expansions of roots, etc. Chapter three is an application of the results, obtained in the previous chapter to the asymptotics and root estimation of some special functions - such as cylindrical functions, $\zeta$-function, $\text{si}(x)$, $\text{ci}(x)$, hypergeometric functions, $\Gamma$-function, orthogonal polynomials, etc. Chapter four is devoted to the asymptotics of some functional equations -- such as nonautonomous equations, intrinsic functions, iterations, etc. The book also contains a lot of examples which are very useful for a student and for an experienced mathematician. The list of references consists of 420 positions.
65H05Single nonlinear equations (numerical methods)
65-02Research monographs (numerical analysis)
65D20Computation of special functions, construction of tables
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
33C15Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$
33C45Orthogonal polynomials and functions of hypergeometric type
33B15Gamma, beta and polygamma functions
11M06$\zeta (s)$ and $L(s, \chi)$