Talk:Bessel–Clifford function

I am afraid I find the first paragraph is unclear in its present form - it says that the B-C function is a function of two complex variables, but does not make it clear. Is n intended to be a complex variable here? If so, isn't that highly unusual? Madmath789 06:59, 13 July 2006 (UTC)

Yes, both n and z are complex variables. I don't know why you call that unusual; several complex variables is a standard topic. Gene Ward Smith 09:33, 13 July 2006 (UTC)

yes, several complex variables certainly is a standard topic - that is not what is unusual. I am referring to the fact that n is very rarely used as the name of a complex variable. I still think the first paragraph is unclear about the two variables and the domain of definition. OK, I have seen the change you have made - it is clearer now. Madmath789 09:42, 13 July 2006 (UTC)

It's certainly true that you don't normally call complex variables "n", but that is commonly done when discussing Bessel functions. Gene Ward Smith 21:37, 13 July 2006 (UTC)

It seems the contour integral for the Bessel-Clifford function (of the first kind) in the final section of this article is erroneous - my guess would be the correct version should be ${\mathcal {C}}_{n}(z)={\frac {1}{2\pi i}}\oint _{C}{\frac {\exp(t+z/t)}{t^{n+1}}}dt={\frac {1}{2\pi }}\int _{0}^{2\pi }\exp(e^{i\theta }+ze^{-i\theta }-in\theta ))d\theta .$. This satifies the recursion and derivative relationships for the Bessel-Clifford function, while the current version doesn't. Related to this, it would be nice if there were more comprehensive references with in-text citations for these functions, in particular, for the relations stated for the Bessel-Clifford functions of the second kind and the integral relation I just mentioned. Bhav Khatri (talk) 12:43, 18 February 2009 (UTC)

To the best of knowledge, Y_n is not proportional to K_n. But the article implies that i^-nY_n(ix)=K_n(x). It does not make sense to me. Am I right about this?

The second kind is of interest. Is there a Taylor series representation, even an ugly non-convergent one? 188.29.164.139 (talk) 13:24, 19 January 2015 (UTC)

Relation with ordinary Bessel function of the second kind

It seems to me that the relationship given between the Bessel-Clifford function of the second kind ${\mathcal {K}}_{n}(x)$ as defined here and the ordinary Bessel function of the second kind $Y_{n}(x)$ cannot possibly be correct. The integral given for ${\mathcal {K}}_{n}(x)$ diverges when $x$ is a negative real number, which includes all the cases corresponding to real arguments of $Y_{n}(x)$. Then, as an earlier unsigned comment pointed out, the relationship given in this article would imply that $K_{n}(ix)=i^{n}Y_{n}(x)$, which is false, even though the similar-looking relation $I_{n}(ix)=i^{n}J_{n}(x)$ is true. Nejssor (talk) 18:12, 4 March 2017 (UTC)