# What is the expanded representation, $\phi(X)$, required to obtain the RBF kernel?

For the two-dimensional case, where $$\boldsymbol X=[x_1, x_2]$$ and its corresponding expanded represetation $$\boldsymbol\phi(X)= [1, \sqrt2 x_1, \sqrt2 x_2, x_1^2, x_2^2, \sqrt2x_1x_2]$$, we can derivate the polynomial function kernel $$K(X,X^T)=<\phi(X),\phi(X)^T>=(1+)^2$$.

What is the expanded representation, $$\boldsymbol \phi(X)$$, required to obtaing the RBF kernel $$K(X,X^T)=<\phi(X),\phi(X)^T>=exp(-\sigma||X-X^T||^2)$$?