Related papers: Symbolic Integration in Weierstrass-like Extension…
The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
In this paper, we present a general method for obtaining addition theorems of the Weierstrass elliptic function $\wp(z)$ in terms of given parameters. We obtain the classical addition theorem for the Weierstrass elliptic function as a…
In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
We enhance the analogy between field extensions and covering spaces by introducing the concept of splitting covering which correspondences to the splitting field in Galois theory. We define semi-topological Galois groups for Weierstrass…
We construct a class of companion elliptic functions associated with the even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $\wp(z|\tau)$ as the blueprint, we will derive their…
Infinite products expansions of the Weierstrass elliptic function \ $\wp(z) = \wp(z,1,\tau)$\ and $n$-order transformations allow us to provide some modular relations.
In this work is we prove model completeness for the expansion of the real field by the Weierstrass $\wp$ function as a function of the variable $z$ and the parameter (or period) $\tau$. We need to existentially define the partial…
The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
We show that the roots of a Weierstrass polynomial on several variables are power series with rational exponents of bounded denominators, whose Newton diagrams are contained in an S-cone. As an application, in Section 4 we deal with some…