OFFSET
-1,4
COMMENTS
Ramanujan's question 754 in the Journal of the Indian Mathematical Society (VIII, 80) asked "Show that exp(x) * x^(-x) * Pi^(-1/2) * Gamma(1 + x) = (8*x^3 + 4*x^2 + x + E)^(1/6), where E lies between 1/100 and 1/30 for all positive values of x".
A numerical search provides an approximate minimum of E = 0.010045071877... at x = 0.6715... (A319458), confirming Ramanujan's lower bound.
REFERENCES
See A319458.
EXAMPLE
0.0100450718774845196884836752168991065136051341...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Sep 19 2018
STATUS
approved