May 29, 2017
We know that the integration rules for exponents breaks down for the case x^-1, and that this case is the log function.
We can recover the exponent rule in the following way: How To Use The Exponent Rules Of Integration To Approximate Log Function
Mathematica has the ability to do arbitrary precision arithmetic, which is an essential thing when attempting to find closed form expressions of decimal numbers. The problem with double precision (16 significant digit) calculations is that it is not near enough precision in most cases to see if there is a repeating pattern in the digits, which is an indication of a rational number. If a decimal number has a repeating pattern of let’s say 100 or 200 digits or more, one cannot see that with 16 digits. This article is going to explore numerical searches for closed form expressions for decimal numbers using the tools provided by Mathematica. Part 1 will be introducing the basic approach and some easy examples. Part 2 will get to harder examples and figuring out how to automate the search in these complicated cases. Using Mathematica to do numerical searches (part 1)