Different definitions of Epanechnikov-Kernel I was just wondering why there are 2 definitions of the Epanechnikov-Kernel. In the first paper, Epanechnikov introduced his kernel [1] with:
$K\left(y\right) = \frac{3}{4 \sqrt{5}} - \frac{3 y^2}{20 \sqrt{5}}$ for $|y| \leq \sqrt{5}$
In the lecture nodes of my course (+ wikipedia) i found following definition: 
$K\left(y\right) = \frac{3}{4} (1 - y^2)$ for $|y| \leq 1$
Is the second one the general case, since we can adjust the size of $y$ with the bandwidth parameter?
Thanks in advance!
[1] http://www.mathnet.ru/links/57ece7df1c1ea5e1484f9abe34a7aefc/tvp1130.pdf :
Epanechnikov, V. A. "Nonparametric estimation of a multidimensional probability density." Teoriya veroyatnostei i ee primeneniya 14.1 (1969): 156-161.
 A: Let's distinguish the two kernels in our notation so we're not using the same symbol for each. So we have
$K^{(e)}\left(y\right) = \frac{3}{4 \sqrt{5}} - \frac{3 y^2}{20 \sqrt{5}}$ for $|y|\leq\sqrt{5}$
and
$K(y)=\frac34 (1−y^2)$ for $|y|\leq 1$
Consider $K_h(y) = \frac{1}{h} K(\frac{y}{h}),\,\text{ for }|\frac{y}{h}|\leq 1$.
By choosing $h=\sqrt{5}$ we get
$K_\sqrt{5}(y) = \frac{1}{\sqrt{5}} \cdot \frac34 (1−\frac{y^2}{5})=\frac{3}{4\sqrt{5}} −\frac{3y^2}{20\sqrt{5}},\, \text{ for }|\frac{y}{\sqrt{5}}|\leq 1$
so they're both the same but with different "base" bandwidth.

Is the second one the general case, since we can adjust the size of y with the bandwidth parameter?

Either may be adjusted with a bandwidth parameter, so they are exactly as general as each other.

As you suggest in comments under your question, this can certainly lead to confusion if you're reading a source that doesn't explicitly define its base (unit bandwidth) kernel, and also doesn't give a reference from which you can obtain it.
I have run into this problem a few times (though usually you can figure it out).
It underlines the importance, when you give a bandwidth, of being explicit about what the unit bandwidth case is.
A: The kernels are the same, except for a different bandwidth.
The version with $\sqrt{5}$ has the benefit of having the standard deviation of 1, meaning that it is more comparable to the Gaussian kernel. The other one, of course, is simpler.
The problem with choosing kernel functions is that you need to adjust the bandwidth $h$ for your kernels. Many (most?) bandwidth estimation techniques are designed for one particular kernel, or for standardized kernels. Depending on the exact kernel you are using, you may need to adjust the bandwidth with the canonical bandwidth for best results.
Unfortunately, the Wikipedia article does not discuss canonical bandwidths, and authors are often not very clear about which bandwidth they specify in their parameters.
The canonical bandwidth of the non-$\sqrt{5}$ version seems to be $15^{1/5}$ from a quick google.
