Related papers: A dozen integrals: Russell-style
This is the solution manual to the odd-numbered exercises in our book "Introducing Monte Carlo Methods with R", published by Springer Verlag on December 10, 2009, and made freely available to everyone.
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7.…
The paper deals with real valued sequences and its distribution on real line.
We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.
Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals {\`a} la…
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers…
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
In one of the three 2010/2011 issues of the journal 'MathematicalSpectrum', this author gave a three-parameter description of the entire set of integral triangles(i.e. triangles with integer side lengths)and with a 120 degree angle.This…
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.
We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
Some new integrals involving the Stieltjes constants are developed in this paper.
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
This paper is an attempt to bring together two approaches to language analysis. The possible use of probabilistic information in principle-based grammars and parsers is considered, including discussion on some theoretical and computational…
Euler evaluates the integrals in the title and recognizes a recursion between them, which he then uses to give continued fractions for the log and arctan. The paper is translated from Euler's Latin original into German.