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</math>
:<math>
\varphi(\mathbf{x})
=
\exp\left(-\frac{1}{2}\|\mathbf{x}\|^2\right)
\left(a^{(0)}_{l_0},a^{(1)}_1,\dots,a^{(1)}_{l_1},\dots,a^{(j)}_{1},\dots,a^{(j)}_{l_j},\dots \right )
</math>
where <math>l_j=\tbinom {k+j-1}{j}</math>,
:<math>
a^{(j)}_{l}=\frac{x_1^{n_1}\cdots x_k^{n_k} }{\sqrt{n_1! \cdots n_k! }} \quad|\quad n_1+n_2+\dots+n_k = j \wedge 1\leq l\leq l_j
</math>
==Approximations==
Because support vector machines and other models employing the [[kernel trick]] do not scale well to large numbers of training samples or large numbers of features in the input space, several approximations to the RBF kernel (and similar kernels) have been introduced.<ref>Andreas Müller (2012). [http://peekaboo-vision.blogspot.de/2012/12/kernel-approximations-for-efficient.html Kernel Approximations for Efficient SVMs (and other feature extraction methods)].</ref>
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