Related papers: On some transforms of trigonometric series

In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…

We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.

We introduce a new method for ``twisting'' relative equivalences of derived categories of sheaves on two spaces over the same base. The first aspect of this is that the derived categories of sheaves on the spaces are twisted. They become…

Based on a reduction processing, we rewrite a hypergeometric term as the sum of the difference of a hypergeometric term and a reduced hypergeometric term (the reduced part, in short). We show that when the initial hypergeometric term has a…

We discuss the convergence problem for coordinate transformations which take a given vector field into Poincar\'e-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these…

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.

Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…

It is known that the sum of the reciprocal of integers, $\sum_n (1/n)$, and the sum of the reciprocal of primes, $\sum_n (1/p_n)$, both diverge. Here, we study a series made from primes that sums exactly to 1. We also show this sum is…

We introduce a shifted convolution sum that is parametrized by the squarefree natural number $t$. The asymptotic growth of this series depends explicitly on whether or not $t$ is a \emph{congruent number}, an integer that is the area of a…

Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by…

The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…

We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences $(a_{n_1...n_d})_{n_1,...,n_d\in\bb N}$ such that for all orthonormal…

Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…

We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to…

We give an equivalent form of the Twin prime conjecture relating to a symmetric property that is observed for terms present in a certain sequence of arithmetic progressions defined for a pair of co-prime integers.