There are several mentions of "closed-form expression" without precisely defining what that means, only "finite combinations of basic operations".

TFA implies that branches (if statements and piecewise statements) are not allowed, but I don't see why not. Seems like a basic operation to me.

Nevermind that `s[i]` is essentially a piecewise statement.

> There are several mentions of "closed-form expression" without precisely defining what that means, only "finite combinations of basic operations".

There is no universal definition of 'closed-form expression'. But there are some basic operations and functions that are broadly accepted, and they are spelled out directly after the 'finite combinations' phrase you quoted from the post. Quoting the remainder of that sentence here:

'[...] finite combinations of basic operations such as addition, subtraction, multiplication, division, integer exponents and roots with integer index as well as functions such as exponentials, logarithms and trigonometric functions.'