weird series notation ANS: Generalized Hypergeometric Functions

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Hi I came across this curious notation on a twitter account (@infseriesbot) that supposedly posts series functions. The notation is very strange to me, hopefully some one who is familiar with this notation can guide me in understanding it. It looks something like this :

series_with_weird_notation

The notation is so weird that I don't know how to query this style in a search engine to learn about it. It seems like its encompassing some kind of series, but I don't know what this style name is to learn about it.

EDIT: ANS -> thanks to @JonathanZ supports MonicaC and @IraGessel for their swift response, these notations are for hypergeometric functions which can under special circumstances specialize into other famous functions, as seen in the comments below :D

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These notations are as @JonathanZ supports MonicaC and @IraGessel points out in the comments are for Generalized Hypergeometric Functions that special-cases into more famous functions like $e^x$, $\sinh (x)$, $\cos(x)$ etc. These hypergeometric functions are more generalized versions of regular geometric series $ \sum_{k=0}^n ar^k$.