![]() Mathematical Functions: A Milestone Is Reached (December 2021)īack when one still had to do integrals and the like by hand, it was always a thrill when one discovered that one’s problem could be solved in terms of some exotic “ special function” that one hadn’t even heard of before. And, yes, Heun functions have a lot of arguments: And they’re very much in vogue now, because they show up in the mathematics of black holes, quantum mechanics and conformal field theory. That might not sound like a big deal, but actually they’re quite a mathematical jungle-for example with 192 known special cases. And now we have Heun functions, that solve equations with four regular singular points. ![]() But in Version 12.1 we’ve generalized that. Typical hypergeometric functions are solutions to differential equations with three regular singular points. Over the years we’ve gradually added a few other kinds of hypergeometric functions (as well as 250 other new kinds of special functions). We covered univariate hypergeometric functions-adding the general pF q case in Version 3.0. Back in Version 1.0 we already had 70 special functions. One long-term story has to do with special functions. And for the Wolfram Language (which also means for Mathematica) we’re always pushing the frontiers of what’s computable in math. Continuous & Discrete Calculus More Math, As Always (March 2020) The contents of this post are compiled from Stephen Wolfram’s Release Announcements for 12.1, 12.2, 12.3 and 13.0. ![]() Here are the updates in symbolic and numeric computation since then, including the latest features in 13.0. Two years ago we released Version 12.0 of the Wolfram Language.
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