Cool! I tried ries on two of my favorite numbers (arising from theory of voting via some difficult integrals which might have a closed form but I used monte carlo) 0.2586333(3) = 0.2586335(4) and 0.1300873(4) = 0.1300876(2) [standard errors in last digit shown in parens] but it didn't find anything I liked. The correct formula (if there is one) may involve erf, e, pi, ln, and algebraic numbers. 0.1300876 = 1/(ln(2)*phi^5) [??] is suitably mysterious, I admit, and does match my accuracy. Then I tried Gosper's (1/4)! and I don't understand how Gosper got his formula. Actually, I practically never understand how Gosper gets his formulas. As I mentioned before, it'd be nice to find formulas for GAMMA(k/48) for example. Such formulas might exist in terms of algebraic numbers and the AGM.