An inequality describing the difference between Gamma and Gaussian distributions is derived. The asymptotic bound is much better than by existing uniform bound from Berry-Esseen inequality.
 V. Koroleva and I. Shevtsova, “An Improvement of the Berry-Essen in Equality with Application to Possion and Mixed Poison Random Sums,” Scandinavian Actuarial Journal, Vol. 2012, No. 2, 2012, pp. 81-105. doi:10.1080/03461238.2010.485370
 R. D. Gordon, “Values of Mills’ Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument,” The Annals of Mathematical Statistics, Vol. 12, No. 3, 1941, pp. 364-366. doi:10.1214/aoms/1177731721