Does any one know how to calculate the following integration? $$ \int_{\mathbb{R}} \left(\exp(z \: e^{-y^2})-1\right)^2 dy=?,\quad z>0. $$ This post is related to my previous question [here][1] , based on which one can have a upper bound. Can any one give an exact solution for this integration? Thanks a lot! Anand [1]: https://mathoverflow.net/questions/161068/has-anyone-seen-this-series