# Talk:Bessel function

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One of the 500 most frequently viewed mathematics articles.

## 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 (talkcontribs)

## Math symbols in section headings

The math symbols in the section headings — are they really needed? I removed them because I think it looks a little bit cluttery, and it makes it difficult to link to subsections from other articles since the math symbols are not plain text, although I noticed that there were redirection pages in order to more easily be able to link to those sections (but it took me a while to realize they existed). I also think the math symbols feel superfluous since they are mentioned in the body text. Or what is the reason they are written in the headings? —Kri (talk) 15:07, 26 February 2015 (UTC)

Many people navigate Bessel and Bessel-related functions by their symbol. This is not true of many functions, but certainly applies here. Limit-theorem (talk) 15:35, 26 February 2015 (UTC)
Okay. —Kri (talk) 15:45, 26 February 2015 (UTC)

## Always a Taylor expansion?

For non-integer order, the powers are non-integral and thus the series for the Bessel function of the first kind isn't a power series, but a Puiseux series or even a Hahn series. Even for integer order, negative orders would make it a Laurent series. Should we change the article to reflect this? It does still hold though that it is the product of ${\displaystyle x^{\alpha }}$ with a Taylor series.--Jasper Deng (talk) 07:12, 5 March 2015 (UTC)

## Confusing introduction to the topic about alpha

In the introduction, the second sentence is very unclear to me: "Although α and −α produce the same differential equation for real α, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α.". The first thing I noticed is that alpha and -alpha produce the same differential equations for all alpha, not just real. The second part of that sentence is very vague/unclear. I hope someone can transform this sentence into something clearer. MicroVirus (talk) 10:24, 8 September 2015 (UTC)

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