#"Decimal factorials are defined by the Gamma function : "#

#Gamma(t) = int_0^oo x^(t-1) e^-x dx#

#"So "Gamma(t+1) = t!#

#"So to calculate 0.5! one must solve the following definite integral"#

#0.5! = int_0^oo sqrt(x) e^-x dx#

#"There exist approximating series, but that is also calculus, so"#

#"i think it cannot be solved without calculus."#

#"There exist good approximating formulas though, like Gosper's"#

#"approximation : "#

#n! ~~ (n/e)^n sqrt(pi(2n+1/3))#

#"(Gosper's approximation is an improvement to Stirling's"# #"formula)"#