Suppose there is a normal distribution and the Gaussian function is $F(x)=\exp(-c\|x-b\|^2)$ where $c$ is a constant and $x,b\in \mathbb{R}^N$, b means the mean value.
$F(x)=\exp(-c\|x-b\|^2)=F(x)=\exp(-c(x^Tx-2x^Tb+b^Tb))=\exp(-c(x^Tx))\times\exp(2cx^Tb)\times\exp(-c(b^Tb))$
1) $F(x_1)+F(x_2)+F(x_3)=\exp(-c(b^Tb)) \times( \exp(-c(x_1^Tx_1))\times\exp(2cx_1^Tb)+\exp(-c(x_2^Tx_2))\times\exp(2cx_2^Tb)+\exp(-c(x_3^Tx_3))\times\exp(2cx_3^Tb) )$
Is there any way I can write as $F(x_1)+F(x_2)+F(x_3)=G(b)\times H(x_1,x_2,x_3)$.
2) How about $\sum\limits_{x\in \Omega}F(x)$?
