Related papers: A note on Sonnenschein summability matrices
For Dirichlet characters $\chi$ mod $k$ where $k\geq 3$, we here give a computable formula for evaluating the mean square sums $\sum\limits_{\substack{\chi \text{ mod }k\\\chi(-1)=(-1)^r}}|L(r,\chi)|^2$ for any positive integer $r\geq 3$.…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
Powers of Fibonacci polynomials are expressed as single sums, improving on a double sum recently seen in the literature.
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th power of positive integers up to n. By means of that we consider the evaluation of the sum of more general series by Bernstein polynomials. Additionally we show the…
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
We obtain simple proofs of certain inequalites for bivariate means.
We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
Paul Van Dooren [Linear Algebra Appl. 27 (1979) 103-140] constructed an algorithm for the computation of all irregular summands in Kronecker's canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary…
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
The simulations of the light scalar mesons on the lattice are presented at the introductory level. The methods for determining the scalar meson masses are described. The problems related to some of these methods are presented and their…
A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two loop sunrise master integrals.
We consider a generalized Gauss sum supported on matrices over a number field. We evaluate this Gauss sum and relate it to the number of totally isotropic subspaces of related quadratic spaces. Then we consider a further generalization of…
We study sums of $k$-potent matrices. We show the conditions by which a complex matrix $A$ can be expressed as a sums of $k$-potent matrices. Also we obtain conditions by which a complex matrix $A$ can be expressed as a sum of finite order…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…