In the reference article of Richard Askey and George Gasper published in the American Journal of Mathematics, Autumn, 1976, Vol. 98, No. 3 (Autumn,1976), pp. 709-737, they attribute on page 731 the following formula to Mehler (quoting a book by Erdelyi): $$ \sum_{n=0}^{\infty}\frac{r^n H_n(x) H_n(y)}{2^n n!}=(1-r^2)^{-1/2} \exp\bigl\{ x^2-\frac{(x-ry)^2}{(1-r^2)} \bigr\}, $$ where $H_n$ is the $n$th Hermite polynomial.

Question: I do not believe that formula, since the lhs is symmetric in $x,y$ whereas the rhs fails to be symmetric in $x,y$. I am also puzzled since, as said above, this article is a reference material for numerous articles on Laguerre and Hermite polynomials.