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)
q-Taylor and interpolation series for Jackson q-difference operators. (English) Zbl 1149.40001

It is outside the scope of a review to give the formulae needed to understand the main results of the paper explicitly. For readers knowledgable in q-theory these main results will be stated below:

A. Let 0<R and f be analytic on Ω R with power series expansion

f(x)= n=0 c n x n ,xΩ R ·

Then f has the q-Taylor expansion

f(x)= k=0 D q k f(a) Γ q (k+1)φ k (x,a),

converging absolutely and uniformly on compact subsets of Ω R .

B. Let f(x) be a function with q-exponential growth of order k,k<lnq -1 , and finite type α,α. Then for a{0}, f(x) has the expansion

f(x)= n=0 (-1) n q -n(n-1)/2 D n q f(aq -n ) Γ q (n+1)φ n (a,x),

converging absolutely and uniformly on compact subsets of .

40A30Convergence and divergence of series and sequences of functions
33D05q-gamma functions, q-beta functions and integrals
39A70Difference operators
47B39Difference operators (operator theory)