Oliver Heaviside, on page 387 of *Electrical Papers*, Vol. I, Macmillan and Co., 1892, available [here](http://archive.org/stream/electricalpapers01heavuoft#page/386/mode/2up), 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?


Any references would be appreciated.



Fourier and Bessel
There is a fundamental reference using Bessel functions in Fourier's works. This is ["Théorie analytique de la chaleur"](http://books.google.it/books?id=TDQJAAAAIAAJ&printsec=frontcover&hl=it#v=onepage&q&f=false) firstly published on 1822. You will find this series firstly given in chapter VI pag. 370. This chapter is about the propagation of the heat in a cylinder ("of course" let me add).


The modern nomenclature was invented by Bessel himself on 1824, just two years after Fourier's work. This is proved in [F. Bessel, "Untersuchung des Theils der planetarischen Störungen", Berlin Abhandlungen (1824)](http://edoc.bbaw.de/volltexte/2008/735/pdf/21hekEZuXxSQ.pdf). Here the functions I and J get their names.


