Related papers: El Logaritmo Integral: N\'umeros primos y algo m\'…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
In this work we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional…
In this survey we discuss a wide variety of aspects related to Lie group integrators. These numerical integration schemes for differential equations on manifolds have been studied in a general and systematic manner since the 1990s and the…
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical…
It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral. We…
We investigate the distribution of the logarithmic derivative of the Riemann zeta-function on the line Re(s)=\sigma, where \sigma, lies in a certain range near the critical line \sigma=1/2. For such \sigma, we show that the distribution of…
The intermediate stage of the development of general relativity is inseparable of Marcel Grossmann's mathematical assistance. Einstein acknowledges Grossmann's help during 1912-1914 to the development of general relativity. In fact, as with…
We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
The Rosenblatt distribution plays a key role in the limit theorems for non-linear functionals of stationary Gaussian processes with long-range dependence. We derive new expressions for the characteristic function of the Rosenblatt…
In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev…
Considered one of the founding fathers of integral geometry, Luis Santal\'o has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in…
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of several equivalent statements} borrowed from algebra, real analysis, general topology, and non-standard analysis. We also…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is…
Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by…
We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
We consider Cauchy type integrals $I(t)={1\over 2\pi i}\int_{\gamma} {g(z)dz\over z-t}$ with $g(z)$ an algebraic function. The main goal is to give constructive (at least, in principle) conditions for $I(t)$ to be an algebraic function, a…
Residues to a given modulus have been introduced to mathematics by Carl Friedrich Gauss with the definition of congruence in the `Disquisitiones Arithmeticae'. Their extraordinary properties provide the basis for a change of paradigm in…
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.