Related papers: Towards a symbolic summation theory for unspecifie…

Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…

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.

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…

A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…

In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

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…

Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…

Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured by Guo and Schlosser and recently confirmed by Jana and…

This paper addresses the problem of video summarization. Given an input video, the goal is to select a subset of the frames to create a summary video that optimally captures the important information of the input video. With the large…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…

In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…

This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…

Back-translation based approaches have recently lead to significant progress in unsupervised sequence-to-sequence tasks such as machine translation or style transfer. In this work, we extend the paradigm to the problem of learning a…

We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…