In addition to the MO question The Ramanujan Problems. , I would like to ask the following.

Problem 754 from the list of the Ramanujan's problems ( http://www.imsc.res.in/~rao/ramanujan/collectedpapers/question/q754.htm ) asks to show that $$e^xx^{-x}\pi^{-1/2}\Gamma(1+x)=(8x^3+4x^2+x+E)^{1/6},$$ where E lies between $\frac{1}{100}$ and $\frac{1}{30}$ for all positive values of $x$. According to http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.9228 (The Problems Submitted by Ramanujan to the Journal of the Indian Mathematical Society, by Bruce C. Berndt, Youn--seo Choi and Soon-Yi Kang) this problem was still open in 1997. What is the status of this problem at present?