Related papers: Generalized universal series
In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
Associated Legendre functions arise in many problems of mathematical physics. By using the generalized Abel-Plana formula, in this paper we derive a summation formula for the series over the zeros of the associated Legendre function of the…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
Translation from the Latin original, "Inventio summae cuiusque seriei ex dato termino generali" (1735). E47 in the Enestrom index. In this paper Euler derives the Euler-Maclaurin summation formula, by expressing y(x-1) with the Taylor…
We prove a generalization of the Edwards-Walsh Resolution Theorem: Theorem: Let G be an abelian group for which $P_G$ equals the set of all primes $\mathbb{P}$, where $P_G=\{p \in \mathbb{P}: \Z_{(p)}\in$ Bockstein Basis $ \sigma(G)\}$. Let…
Recently, in [Bor4], Bor proved a main theorem dealing with $|\bar{N}, p_{n}|_{k}$ summability factors of infinite series. In the present paper, we have generalized that theorem for $|A, p_{n}|_{k}$ summability method by taking normal…
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
We review recent results on the Cauchy-Kowalevsky structure of theories with higher derivatives in vacuum. We prove genericity of regularity of solutions under the assumption of analyticity. Our approach is framed in the general context of…
We prove that a Poisson-Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane of finite order. These formulas simultaneously generalize the classical Poisson formula…
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
This is the first in a set of three papers providing an introduction to generalised Cesaro convergence. We start with traditional Cesaro methods for extending classical convergence and further generalise these to allow the calculation of…
We shall consider some special generalizations of Euler's factorial series. First we construct Pad\'e approximations of the second kind for these series. Then these approximations are applied to study global relations of certain p-adic…
In this paper we consider a question on existence of double Walsh series universal in weighted $L_\mu^1[0,1]^2$ spaces. We construct a weighted function $\mu(x,y)$ and a series by double Walsh system of the form $$\sum_{n,k=1}^\infty…
We define some generalizations of the classical descent and inversion statistics on signed permutations that arise from the work of Sack and Ulfarsson [20] and called after width-k descents and width-k inversionsof type A in Davis's work…
We show how to extend the theory of generalized Reynolds ideals, as introduced by B. K"ulshammer, from symmetric algebras to arbitrary finite-dimensional algebras (in positive characteristic). This provides new invariants of the derived…
An integer of the form $p_m(x)= \frac{(m-2)x^2-(m-4)x}{2} \ (m\ge 3)$, for some integer $x$ is called a generalized polygonal number of order $m$. A ternary sum $\Phi_{i,j,k}^{a,b,c}(x,y,z)=ap_{i+2}(x)+bp_{j+2}(y)+cp_{k+2}(z)$ of…
In this paper we consider the question of existence of trigonometric series universal in weighted $L^1_{\mu}[0,2\pi]$ spaces with respect to rearrangements and in usual sense.
We study binomially weighted summation methods given by \[ (x_n)_{n\in \mathbb{N}} \mapsto \left(\sum_{k=0}^n\binom{n}{k}r^k(1-r)^{n-k}x_k\right)_{n\in \mathbb{N}} \] for $r\in (0,1)$, and their behavior under composition with summation…