In #18696 there is a problem of having `Piecewise(...).is_hypergeometric` 
return True when all the expressions it contains are hypergeometric. 
Quoting from my comment there:

The `is_hypergeometric` function has to be made to look for a `Piecewise` 
> and return True if all the expressions in the `Piecewise` are 
> hypergeometric. But better, `Piecewise` should be able to respond to all 
> `is_what` requests by returning a value based on all its args meeting that 
> criteria. `Piecewise` already knows how to handle a rewrite request (e.g. 
> `Piecewise((factorial(x),x>0),(1,True)).rewite(gamma)` works. I believe the 
> `core.basic.rewrite` and `core.basic._eval_rewrite` are able to work out 
> how to rewrite the args of Piecewise without Piecewise having all 
> `_eval_rewrite_as_what`. It would be good if we could do the same thing for 
> all `is_what` properties.


What would be the best way to get Piecewise to do this?

/c 

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