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

Definite Integration in Mathematica V3.0

An article

One of the charms of mathematics is that it is possible to make elementary discoveries about objects that have been studied for millenia. A most striking example occurred recently when David Bailey of NASA/Ames and Peter Borwein and Simon Plouffe of the Centre for Experimental and Computational Mathematics at Simon Fraser University (henceforth, BBP) discovered a remarkable, and remarkably simp...

Investigation of Wagon Derailment Moving on Random Rail Irregularities using Nonlinear 3-Dimentional Model (RESEARCH NOTE)

Rail irregularity is one of the most effective factors in train derailment. theste irregularities have generally random distribution that are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probabiliy densities and zero mean values. The quality of irregularities, their distribution along the rails and wagon speed are the main factors for train derailment ...

The Evaluation of Integrals of Bessel Functions via G-function Identities

A few transformations are presented for reducing certain cases of Meijer’s Gfunction to a G-function of lower order. Their applications to the integration of a product of Bessel functions are given. The algorithm has been implemented within Mathematica 3.0.

Towards an automation of the circle method

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are pr...