Recognizing Numerical Constants

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Abstract:

The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. These techniques will be illustrated by discussing the authors' work in recognizing Euler sums and in finding new formulas for $\pi, \pi^2 and \log^2{(2)}$, formulae that permit digits to be extracted from their expansions.