Related papers: A dozen integrals: Russell-style

This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…

Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.

Over the years various errors have been identified in the 1980 paper of James on the groups of order $p^6$, where $p$ is an odd prime. Here we summarise them.

We review a special technique for evaluating challenging integrals by providing a number of examples. Many of our examples prove integrals from the popular table of Gradshteyn and Ryzhik.

We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

We consider compositions of natural numbers when there are different types of each natural number. Several recursions as well as some closed formulas for the number of compositions is derived. We also find its relationships with some known…

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.

This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…

This collection of sums and integrals has been harvested from the mathematical and physical literature in unstructured ways. Its main use is backtracking the original sources whenever an integral of the reader's application resembles one of…

This is the original paper appeared in the book "Elliptic and Parabolic Methods in Geometry (Minneapolis, MN,1994), A K Peters, Wellesley, MA, (1996)" (p.1-16), except with a few minor modifications as described at the end of the paper (on…

In 2001-2002, I happened to have proposed a new definite integral in the American Mthematical Monthly (AMM),which later came to be known in my name (Ahmed). In the meantime, this integral has been mentioned in mathematical encyclopedias and…

This is a 1971 dissertation. Only its extended abstract was published at the time. While some results appeared in other publications, a number of details remained unpublished and may still have relevance.

We use a representability theorem of G. L. Watson to examine sums of squares in Quaternion rings with integer coefficients. This allows us to determine a large family of such rings where every element expressible as the sum of squares can…

Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have been studied in works of M.-- C. Chang, B. Green and the author. In the paper we…

In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of…

These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne…

These are extended notes of a lecture about the papers 1207.1883 by Esnault-Levine-Wittenberg and 1308.3024 by Wittenberg. The aim is to define the Esnault-Levine-Wittenberg indices, establish their basic properties amd to pose several…

This is an overview article on the Kontsevich integral written for the Encyclopedia of Mathematical Physics, to be published by Elsevier.