The simplify/GAMMA function is used to simplify expressions containing the Gamma, factorial, or binomial functions.

simplify/GAMMA will convert any factorials or binomials in expr to GAMMAs before proceeding with the simplification. If the result is required to be in factorial form, simplify/factorial can be used instead.

You can enter the command simplify/GAMMA using either the 1-D or 2-D calling sequence.  For example, simplify(GAMMA(n+1)/GAMMA(n), GAMMA) is equivalent to $\mathrm{simplify}\left(\frac{\mathrm{\Gamma }\left(n+1\right)}{\mathrm{\Gamma }\left(n\right)}\,\mathrm{\Gamma }\right)$.

$\mathrm{simplify}\left(\frac{\mathrm{\Gamma }\left(n+1\right)}{\mathrm{\Gamma }\left(n\right)}\,\mathrm{\Gamma }\right)$

$n$

$\mathrm{simplify}\left(\mathrm{\Gamma }\left(n+1\right)\left(n^2+3n+2\right)\,\mathrm{\Gamma }\right)$

$\mathrm{\Gamma }\left(n+3\right)$

$\mathrm{simplify}\left(\mathrm{\Gamma }\left(n+2\right)\left(n^2+5n+6\right)\,\mathrm{\Gamma }\right)$

$\mathrm{\Gamma }\left(n+4\right)$

$\mathrm{simplify}\left(n!\left(n^2+3n+2\right)\,\mathrm{\Gamma }\right)$

$\mathrm{\Gamma }\left(n+3\right)$