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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?

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Look at the first paragraph in this mathworld entry for Bessel functions. It appears that you should consult Cajori's book from the references given there. –  Adrián Barquero Apr 15 '11 at 22:14
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Well, it's the notation used by Bessel himself, see here. As to why Bessel used this notation, a cursory glance seems to indicate that he was just following the alphabet. –  t.b. Apr 16 '11 at 7:32
    
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. –  J. M. Apr 16 '11 at 16:58
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@t.b., can you add your comment as an answer? –  Tobin Fricke Mar 21 '12 at 10:47

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