Thinking to Liouville's constant I was hoping If we can find with the decimal of the famous constant a function wich vanish at these decimals .
I found currently a very simple function wich is :
$$f\left(x\right)=\left(10^{-1!}-x\right)\left(10^{-2!}-x\right)\left(10^{-3!}-x\right)...$$
Can we find a more "sophisticated" example ?Is there bigger maths here ?
Thanks in advance .
Edit : By more "sophisticated" I mean we cannot use this "canonical" function just in adding or composing or multiplying this function with another . "Un dépaysement soudain" as Grothedieck could wrote is needed.