 GAMMA - Maple Help

simplify/GAMMA

simplifications involving the GAMMA, factorial, or binomial functions Calling Sequence

 simplify(expr, GAMMA) $\mathrm{simplify}\left(\mathrm{expr},\mathrm{\Gamma }\right)$ Parameters

 expr - any expression GAMMA - literal name; GAMMA Description

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

 > $\mathrm{simplify}\left(\frac{\mathrm{GAMMA}\left(n+1\right)}{\mathrm{GAMMA}\left(n\right)},\mathrm{GAMMA}\right)$
 ${n}$ (1)
 > $\mathrm{simplify}\left(\mathrm{GAMMA}\left(n+1\right)\left({n}^{2}+3n+2\right),\mathrm{GAMMA}\right)$
 ${\mathrm{\Gamma }}{}\left({n}{+}{3}\right)$ (2)
 > $\mathrm{simplify}\left(\mathrm{GAMMA}\left(n+2\right)\left({n}^{2}+5n+6\right),\mathrm{GAMMA}\right)$
 ${\mathrm{\Gamma }}{}\left({n}{+}{4}\right)$ (3)
 > $\mathrm{simplify}\left(n!\left({n}^{2}+3n+2\right),\mathrm{GAMMA}\right)$
 ${\mathrm{\Gamma }}{}\left({n}{+}{3}\right)$ (4)