On 7/9/2013 9:50 PM, Nasser M. Abbasi wrote: > Speaking of independent integration test suite. I have an old > dover book with over 2,000 indefinite integrals and their > solutions. Book is called > > "A new table of indefinite integrals computer processed" > by Melvin Klerer and Fred Grossman ISBN 0-486-62714-4 1971 > > I scanned one page of the book (with the covers) here as > an example: > > http://12000.org/tmp/070913/sample.pdf > > According to the book, these are all verified and correct. >
You might read more carefully what they mean by verified. (And report back here). As I recall, all they did was some random numerical evaluation, hardly the kind of checking that would confirm behavior at singularities etc.
Also, the text is available free online for Gradshteyn and Ryzhik, which I believe contains many more integrals. Perhaps Klerer could not confirm them or thought they were not so useful?
I suggest that the G&R compact disk be used as a test suite. However, tricks like change of variables are presumed, so that a skilled human can make use of G&R where a less-skilled computer will fail to notice that a problem is tabulated.
There is an even larger multi-volume table, in Russian, of many obscure integrals, generally so poorly printed that formulas might easily be misread. I am under the impression that these generally fall out of algorithms involving Meijer G functions, which was how they were generated (by hand). [I have vols 1-3) See...
A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev. Integrals and Series. First edition (Russian), volumes 1?5, Nauka, 1981?1986. First edition (English, translated from the Russian by N.M. Queen), volumes 1?5, Gordon & Breach Science Publishers/CRC Press, 1988?1992, ISBN 2-88124-097-6. Second revised edition (Russian), volumes 1?3, Fiziko-Matematicheskaya Literatura, 2003.
Note that O.I. Marichev was hired by Wolfram in 1992, and the algorithms used to generate these formulas may now be found in one or more computer algebra systems.