Special functions are in a sense a way of packaging mathematical knowledge: once you know that the solution to your equation is a Lamé function, that immediately tells you lots of mathematical things about it. 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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