FoxH: A New Super Special Function

The Wolfram Language has over 250 mathematical functions, including well-known elementary and special functions. Most of these mathematical functions might be considered as specific cases of very general superfunctions like the G-function or MeijerG, which was introduced in Version 3 of Mathematica. However, for various applications we need even more powerful superfunctions. For Version 12.3, we have introduced the FoxH function that is a natural generalization of MeijerG and plays an important role in problems of statistics and symbolic integration. FoxH is also able to represent functions that are not expressible in terms of MeijerG , such as the Mittag-Leffler function and others. For the upcoming release we have implemented the Fox HReduce function, which can be used to represent functions in terms of FoxH , and also improved Fox itself. I will give an elementary introduction to FoxH and its applications during the talk.