Related papers: On some Integrals associated with the Riesz functi…

In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.

As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a…

We introduce the notion of unbounded locally solid Riesz spaces, and investigate its fundamental properties.

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…

We deduce new properties of the orbicyclic function $E$ of several variables investigated in a recent paper by V. A. Liskovets. We point out that the function $E$ and its connection to the number of solutions of certain linear congruences…

We present in this survey some results regarding Riemann_Lebesgue integrability with respect to arbitrary non-additive set functions.

This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…

This preprint concerns Banach spaces of functions converging at infinity. In particular, spaces of continuous functions, Lebesgue spaces and sequence spaces. In each framework we show versions of Riesz's representation theorem.

In the paper, the authors find some integral representations and discover some properties of Lah numbers.

We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.

We characterize Riesz frames and frames with the subframe property and use this to answer most of the questions from the literature concerning these properties and their relationships to the projection methods etc.

In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some…

Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.

Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.

In this short article we present some properties regarding the order and the type of an entire function.

We present some bounds of the inverses of tails of the Riemann zeta function on $0 < s < 1$ and compute the integer parts of the inverses of tails of the Riemann zeta function for $s=\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$.

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…

In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…

Following a recent paper by X. Tolsa and A. Ruiz de Villa [Non existence of principal values of signed Riesz transforms of non integer dimension, preprint], we show that the finiteness of square function associated with the Riesz transforms…

Using a generalized Littlewood theorem concerning integrals of the logarithm of analytical functions, we have established a few equalities involving integrals of the logarithm of the Riemann Zeta-function and have rigorously proven that…