Oliver Heaviside, on page 387 of *Electrical Papers*, Vol. I, Macmillan and Co., 1892, available here, writes

$$v = 1 - \frac{n^2r^2}{2^2} + \frac{n^4r^4}{2^2 4^2} - \frac{n^6r^6}{2^24^26^2} + \ldots = J_0(nr)$$

and

**This function is usually denoted by $J_0(nr)$, and was first employed by Fourier. Whether he invented it or discovered it is a doubtful point; the question is raised whether mathematical truths lie within the human mind alone, or whether the infinite body of known and unknown mathematics could exist in a dead universe. But this is metaphysics, which is all vanity and vexation of spirit.**

Heaviside gives no reference.

I have two questions:

- Are there any references in the Fourier work about the symbol $J_0()$ ?
- What does the letter $J$ stand for?

Any references would be appreciated.