Add to ORKGFor a certain class of power series, infinite products, and Lambert type series, we establish a necessary and sufficient condition for the infinite set consisting of their values, as well as their derivatives of any order at any algebraic points except their poles and zeroes, to be algebraically independent. As its corollary, we construct an example of an infinite family of entire functions of two variables with the following property: Their values and their partial derivatives of any order at any distinct algebraic points with nonzero components are algebraically independent
After defining in detail the Lambert $W$-function branches, we give a large number of exact identiti...
The paper is concerned with the transcendental numbers. The aim is to prove the algebraic independen...
Abstract We prove algebraic independence of functions satisfying a simple form of algebraic Mahler f...
For a certain class of power series, infinite products, and Lambert type series, we establish a nece...
Abstract Algebraic independence of values of certain infinite products is proved, where the transcen...
International audienceIn this paper, the algebraic independence of values of the functionG d (z) := ...
We construct a complex entire function with arbitrary number of variables which has the following pr...
Abstract We study infinite products \(F(z)=\prod_{j\ge0}p(z^{d^j})\), where \(d\ge2\) is an integer...
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
This paper gives conditions for algebraic independence of a collection of functions satisfying a cer...
In this paper, we give a new criterion for the algebraic independence of the values of power series....
This thesis is concerned with the problem of determining a measure of algebraic independence for a p...
AbstractWe extend a result of J.-P. Allouche and O. Salon on linear independence of formal power ser...
AbstractLet f(z) = Σk = 0∞ zk!. Then in p-adic field we prove that for any algebraic numbers α1 ,…, ...
Two representations of a complex number via a Cantor series and a Cantor product are introduced. The...
After defining in detail the Lambert $W$-function branches, we give a large number of exact identiti...
The paper is concerned with the transcendental numbers. The aim is to prove the algebraic independen...
Abstract We prove algebraic independence of functions satisfying a simple form of algebraic Mahler f...
For a certain class of power series, infinite products, and Lambert type series, we establish a nece...
Abstract Algebraic independence of values of certain infinite products is proved, where the transcen...
International audienceIn this paper, the algebraic independence of values of the functionG d (z) := ...
We construct a complex entire function with arbitrary number of variables which has the following pr...
Abstract We study infinite products \(F(z)=\prod_{j\ge0}p(z^{d^j})\), where \(d\ge2\) is an integer...
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
This paper gives conditions for algebraic independence of a collection of functions satisfying a cer...
In this paper, we give a new criterion for the algebraic independence of the values of power series....
This thesis is concerned with the problem of determining a measure of algebraic independence for a p...
AbstractWe extend a result of J.-P. Allouche and O. Salon on linear independence of formal power ser...
AbstractLet f(z) = Σk = 0∞ zk!. Then in p-adic field we prove that for any algebraic numbers α1 ,…, ...
Two representations of a complex number via a Cantor series and a Cantor product are introduced. The...
After defining in detail the Lambert $W$-function branches, we give a large number of exact identiti...
The paper is concerned with the transcendental numbers. The aim is to prove the algebraic independen...
Abstract We prove algebraic independence of functions satisfying a simple form of algebraic Mahler f...