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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:

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

Any references would be appreciated.

2 corrected spelling of a tag
1

# Fourier and Bessel

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:

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

Any references would be appreciated.