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 $${\mathcal C}_n(z) = \frac{1}{2 \pi i} \oint_C \frac{\exp(t+z/t)}{t^{n+1}} dt = \frac{1}{2 \pi}\int_0^{2 \pi} \exp(e^{i\theta}+z e^{-i\theta}-in\theta))d\theta.$$. 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, Yn is not proportional to Kn. But the article implies that i-nYn(ix)=Kn(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 $$K_n(ix)=i^nY_n(x)$$, which is false, even though the similar-looking relation $$I_n(ix)=i^nJ_n(x)$$ is true. Nejssor (talk) 18:12, 4 March 2017 (UTC)