
We now present a gallery of formulas produced by our algorithm. While our algorithm has been used to compute thousands of representations for , we must limit ourselves here to putting on display just a small number of these representations. To make a point of the strength of our algorithm, we've selected examples which are not listed in Integrals and Series, Volume 3: More Special Functions [7], cannot be computed by Mathematica 2.2's HypergeometricPFQ function, and cannot be computed by Maple 5.3's hypergeom function. Macsyma 419.0's hgfred function is able to make progress on the first, third, and fourth examples (for the latter two choosing representations in terms of whittakerm and alegendrep) but is unable to eliminate hyperf from the remaining examples. These examples are all quite typical of the formulas that can be produced by our algorithm.


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