Talk:Bessel function

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How to derive the Integral representation of Bessel functions of the second kind from its definition Y(x)={Jn(x)cos(n times pi)-J-n(x)}/sin(n times pi) with n tends to a integer ? I eager to know the proof because the Integral representation explain the asymptotic behaviour of Y with large x. —Preceding unsigned comment added by 61.18.170.29 (talk • contribs)

It strikes me that there are numerous references to Mathematica in many of the plots. I consider this a sneaky type of advertisement, which does not belong in a Wikipedia page. I already had bad experiences with the aggressive commercial branch of Wolfram in the past and so was a little shocked to see their influancde also popping up here. Actually, the same pictures or better can also be made by WxMaxima or Maple, so why refer to the package so many times? 130.161.210.156 (talk) 12:26, 13 January 2023 (UTC)Reply

Agreed. In fact only two such references remained, and I have deleted both. catslash (talk) 01:30, 7 August 2025 (UTC)Reply

There is a suggestion to make it easier for non-technical readers, though keeping the technical part. Since drums are well known, even to non-technical readers, it might be possible to start with an explanation of them. The modes of square drum heads are easier to calculate and visualize. Maybe octagonal ones are not so hard, and in between square and circle? In any case, visualizing the modes might help people understand them. Gah4 (talk) 21:29, 29 May 2025 (UTC)Reply

The article about E. T. Whittaker notes that he provided a general expression for Bessel functions as integrals involving Legendre functions. It's not shown here. Van.snyder (talk) 21:43, 6 August 2025 (UTC)Reply

My impression is that it derives from standard integral representations of Bessel functions in Watson and Whittaker, after a change of variables. (Erdelyi may provide more explicit formulae.) Tito Omburo (talk) 22:05, 6 August 2025 (UTC)Reply

I had a hard time finding some basic properties of Bessel functions of the first kind. In particular, the orthogonality relation and if the functions are even or odd. I would suggest adding something similar to a "main properties" section like in the page for Legendre polynomials. This article would also benefit from clearer structure in general. Tastamo (talk) 20:19, 23 February 2026 (UTC)Reply