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Apr 18, 2005 - 100,000+ Hypergeometric Formulas Previous Next

It always helps to have some results when trying to push a Ph.D. thesis past a university committee. With this in mind, I am very pleased to announce the availability of

100,000+ HYPERGEOMETRIC FORMULAS

on my Planet Quantum web site.

I created these formulas using my computer algebra system Quantum. My ISSAC 96 algorithm played a big role.

I used symbolic linear algebra, multivariate polynomial factorization, multivariate polynomial gcd, partial fraction decomposition, high precision numerical evaluation, special functions, integration, differentiation, integer factorization, the LLL algorithm, Simon Plouffe et. al.'s Inverse Symbolic Calculator, Neil Sloane's On-Line Encyclopedia of Integer Sequences, and many books and references including the indispensable and legendary book Prudnikov, A. P., Brychkov, Yu. A., Marichev, O. I. (1990), Integrals and Series, Volume 3: More Special Functions, Gordon and Breach Science Publishers.

The online publication of the formulas was also quite a chore. I used TeX, dvipng, optipng, Dreamweaver, and a lot of specialized custom code which I implemented in my Quantum language which allowed me to automate the process as much as possible. I had to switch ISP's and learn how to configure accounts, FTP, and Apache on a FreeBSD virtual server.

Where do I go from here? The next step in my plan is the online publication of

100,000+ INTEGRALS

I have a lot of Risch, MeijerG infrastructure in place and working. A large online integral table would be a great online resource and a powerful demonstration of my work. Therefore, 100,000+ INTEGRALS is my exciting next goal to accomplish.

I thank all my supporters for their patience while I completed my 100,000+ hypergeometric formulas project. There is much more excitement ahead and I promise to chat with you again.



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