BBP-type formulas — An elementary approach

A Compendium of BBP-Type Formulas for Mathemati al Constants

Kovalevskaya top – an elementary approach

The goal of this note is to give an elementary and very short solution to equations of motion for the Kovalevskaya top [1]. For this, we use some results from the original papers by Kovalevskaya [1], Kötter [2] and Weber [3] and also the Lax representation from the note [4]. 1. The Kovalevskaya top [1] is one of the most beautiful examples of integrable systems. This is the top for which the pr...

The power of Mathematica for investigation of BBP, Adamchik-Wagon, Chudnovsky’s, and Ramanujan formulas of Pi

The BBP, BBP-type, Adamchik-Wagon, Chudnovsky's, and Ramanu-jan formulas of Pi are investigating by Mathematica. We point out errors of two BBP-like formulas.

FINDING AND EXCLUDING b-ARY MACHIN-TYPE BBP FORMULAE

Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, and there are hints that they should be normal numbers, i.e., that their base b digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call Machin-type BBP formulae, for which it relatively easy to...

An elementary approach to subresultants theory

In this paper we give an elementary approach to univariate polynomial subresultants theory. Most of the known results of subresultants are recovered, some with more precision, without using Euclidean divisions or existence of roots for univariate polynomials. The main contributions of this paper are not new results on subresultants, but rather extensions of the main results over integral rings ...