We prove that a Gaussian Taylor series takes almost surely every complex value with at most one exception. This presents an answer to a problem of Kahane. We also present an example to show some differences between Gaussian and classical Taylor series.
"On a Problem of Kahane About the Image of Gaussian Taylor Series." Ann. Probab. 15 (3) 1203 - 1209, July, 1987. https://doi.org/10.1214/aop/1176992091