5
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The $n$th Bessel function of the first kind is usually denoted $J_n(x)$.

Where did the use of the letter $J$ to indicate the Bessel function come from?

  • 0
    Look at the first paragraph in this mathworld entry for [Bessel functions](http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html). It appears that you should consult Cajori's book from the references given there.2011-04-15
  • 5
    Well, it's the notation used by Bessel himself, see [here](http://books.google.com/books?id=oG7NAAAAMAAJ&dq=Bessel%2C%20Untersuchung%20des%20Theils%20der%20planetarischen%20St%C3%B6rungen%2C%20Berlin%20Abhandlungen%20(1824)&pg=RA1-PA41#v=onepage&q&f=false). As to why Bessel used this notation, a cursory glance seems to indicate that he was just following the alphabet.2011-04-16
  • 0
    On the other hand, for the "second kind" Bessel functions, $N_\nu(z)$ was used, for "Neumann"; how they became denoted $Y_\nu(z)$ I have forgotten. I'll check my handbooks and report back.2011-04-16
  • 3
    @t.b., can you add your comment as an answer?2012-03-21

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