Related papers: Poisson summation formulas: A new approach
We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate…
This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
We establish several summation formulae for hypergeometric and basic hypergeometric series involving noncommutative parameters and argument. These results were inspired by a recent paper of J. A. Tirao [Proc. Nat. Acad. Sci. 100 (14)…
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial approximations for functions in these…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…
In this paper we find explicit formulas for the Poisson and heat semigroups associated to the modified Bessel operator and on the hyperbolic spaces $\mathbb{H}^n$.
We discuss perturbative solutions of renormalization group equations, and propose the use of resummation scale techniques in assessing theoretical uncertainties on the extraction of parton distribution functions from data.
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of…
The aim of the present work is to provide a supplement to the authors' paper (2018). It is shown that our results on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the…
In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential…