Bessel Function of the First Kind/Instances/Order 0

Specific Instance of Bessel Functions of the First Kind
Let $\map {J_n} x$ denote the Bessel function of the first kind of order $n$.

Proof
From Series Expansion of Bessel Function of the First Kind:

where $n$ is not a (strictly) negative integer.

$0$ fits that category, and so:

Or working directly upon the terms themselves: