Talk:Bessel function

Integral representation of Bessel functions of the second kind

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)

Many annoying references to Mathematica

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)

1. Numbered list item

Origin of Bessel functions

@Limit-theorem: thanks for adding a reference to Bernoulli. Could you expand on when he did so? I see that the cited article talks about James Bernoulli and not Daniel. ReyHahn (talk) 11:31, 9 February 2025 (UTC)

1732, According to [1], p. 111. That article probably contains enough for a History section, if someone were inclined to add it. XabqEfdg (talk) 12:06, 9 February 2025 (UTC)

But that is not the same article cited? Could somebody verify it is in the other article? or should we replace the citation? --ReyHahn (talk) 08:33, 10 February 2025 (UTC)

Limiting form of $J_{\alpha }(z)$ for small $z$

For the case of if $\alpha$ is a positive integer (one term dominates unless $\alpha$ is imaginary), there is a term with factor $\cot \alpha \pi$, which doesn't make any sense because it is infinite. Also, how can $\alpha$ be imaginary if it is a positive integer? There must be a mistake. I suggest copying the asymptotic form from NIST. UlyssesZhan (talk) 03:48, 7 April 2025 (UTC)

technical

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)