Unpublished memo: Density of the product of two real Gaussian random variables. This result is mentioned in the paper On the Frequency Function of $xy$, by Cecil C. Craig, Ann. Math. Statist. Volume 7, Number 1 (1936), 1-15, where it is said to be ``well-known'' and attributed to a 1932 paper by J. Wishart and M. S. Bartlett.