Related papers: On certain maps defined by infinite sums
The present note considers a certain family of sums indexed by the set of fixed length compositions of a given number. The sums in question cannot be realized as weighted compositions. However they can be be related to the hypergeometric…
In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…
We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to…
We introduce a model of simple type theory with potential infinite carrier sets. The functions in this model are automatically continuous, as defined in this paper. This notion of continuity does not rely on topological concepts, including…
The present article deals with properties of a certain function of the Minkowski type with arguments defined by Engel series. Differential, integral, and other properties of the function were considered.
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
We provide a characterization of when a countably infinite set of finite sets contains an infinite sunflower. We also show that the collection of such sets is Turing equivalent to the set of programs such that whenever the program converges…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
We use an elementary argument to prove some finite sums involving expressions of the forms $(q)_n$ and $(a;q)_n$ along with inductive formulas for some sequences.
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…