GAUSSIAN
\begin{equation}
\kernel(z)= \frac{1}{\sqrt{2\pi} }e^{-z^2/2} .
\end{equation}
EPAN2
\begin{equation}
\kernel(z) = \left\{
\begin{array}{ll}
\frac{3}{4}(1-z^2), & |z| < 1\\
0, & \mathrm{otherwise}
\end{array}\right. .
\end{equation}
EPANECHNIKOV
This kernel is the same as EPAN2 but has support on a wider interval
\begin{equation}
\kernel(z) = \left\{
\begin{array}{ll}
\frac{3}{4}(1-\frac{1}{5}z^2)/\sqrt{5}, & |z| < \sqrt{5}\\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}
BIWEIGHT
\begin{equation}
\kernel(z) = \left\{\begin{array}{ll}
\frac{15}{16}(1-z^2)^2, & |z| < 1\\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}
RECTANGLE
\begin{equation}
\kernel(z) = \left\{\begin{array}{ll}
1/2, & |z| < 1 \\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}
TRIANGLE
\begin{equation}
\kernel(z) = \left\{\begin{array}{ll}
1-|z|, & |z| < 1 \\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}
COSINE
\begin{equation}
\kernel(z) = \left\{\begin{array}{ll}
1+\cos(2\pi z), & |z| < 1/2 \\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}
PARZEN
\begin{equation}
\kernel(z)=\left\{\begin{array}{ll}
\frac{4}{3}-8 z^2 + 8|z|^3, & |z| \le 1/2 \\
\frac{8}{3}(1-|z|)^3, & 1/2 < |z| \le 1\\
0, & \mathrm{otherwise}
\end{array}\right.
\end{equation}