Define an anonymous function approx$\_$factorial which will calculate an approximate

value of n$!$ using the first three terms of the Stirling series:

n $!2$ n$($ n

e $)$n

$(1+1$

$12$ n $+1$

$288$ n$2)$

The function should be able to take vector input, e$.$g$.$

$>>$ approx$\_$factorial$(1$:$6)$

ans $=$

$1\mathrm{.}00222\mathrm{.}00066\mathrm{.}000624\mathrm{.}001120720\mathrm{.}01$

Calculate the relative error of the approximations for n $=1,2,3,...,8$