Related papers: Composition sums related to the hypergeometric fun…
We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…
Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…
We show that on real algebraic sets algebraically constructible functions coincide with the finite sums of signs of polynomials. Then we give some applications.
We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In…
We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted…
In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing…
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's.…
The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Partly due to their unusual arithmetic properties, these…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…