# How to find a function with the following properties?

I want to find a function $f(s,x)$ such that

• $f(s,x)$ is analytic

• for any $s \in Z^+$,
$f(s,x)=B_s(x)$, where $B_s(x)$ are the Bernoulli polynomials

• $f(a, x)$ is elementary against $x$ at any constant $a$

• If possible, $f(s,b)$ is elementary against $s$ at any constant $b$

The last condition is not mandatory.

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