### Program v akademickém roce 2021/2022

30. 9. 2021, 11:25 - 12:10

Petr Blaschke, Hypergeometrization.

The seminar will be held online via Google Meet link https://meet.google.com/yky-qxgf-xob

Abstract:
We will introduce and discuss properties of "hypergeometrization", i.e. an operator acting on smooth functions given by
$$f\left(\begin{array}{c} a \\ c \end{array};x\right):=\sum_{k=0}^{\infty}\frac{f^{(k)}(x)}{k!} \frac{(c-a)_k}{(c)_k}(-x)^k,$$
where $c$, $a$ are given numbers and $f$ is a smooth function.

Generalized hypergeometric functions and their multivariate generalization can obtained by successive application of this operator on elementary functions. Hypergeometrization also converts an elementary identity into transformation rule of special functions. Finally, properties of the operator can link together many seemingly disconnected identities. For instance, from a single property of hypergeometrization (a special case of change of variable) we can deduce Pfaff transform, quadratic transform of 2F1, reduction of Appell˙s F1 to 3F2 and to 2F1, link between G2 and F1 functions and many more.