I am having some trouble simplifying some Gamma functions. I have a large expression in which some combinations of Gamma functions appear, that can be simplified, but applying FullSimplify
won't give the desired result.
As an example, this combination appears:
(111 Gamma[5/4]^3)/(-96 Gamma[9/4]^3 + 40 Gamma[5/4]^2 Gamma[13/4])
after applying FullSimplify
,
FullSimplify[(111 Gamma[5/4]^3)/(-96 Gamma[9/4]^3 + 40 Gamma[5/4]^2 Gamma[13/4])]
(* (111 Gamma[5/4]^3)/(-96 Gamma[9/4]^3 + 40 Gamma[5/4]^2 Gamma[13/4]) *)
Although, if I consider the inverse expression, the simplification goes well,
FullSimplify[(-96 Gamma[9/4]^3 + 40 Gamma[5/4]^2 Gamma[13/4])/(111 Gamma[5/4]^3)]
(* -(25/37) *)
I guess that this is due to the sum in the numerator, so the fraction can be expanded, then Mathematica recognises the to ratios of Gamma functions and simplify them separatedly.
I have tried with FunctionExpand
, Expand
, Apart
... and didn't get any result. Any advice?
FullSimplify[(111 Gamma[5/4]^3)/(-96 Gamma[9/4]^3 + 40 Gamma[5/4]^2 Gamma[13/4])] //. {Gamma[x_] /; x > 1 -> (x - 1) Gamma[x - 1]}
. (Using a conditional rule.) And actually for this exampleFullSimplify[]
is not needed to get the desired answer. $\endgroup$1/FullSimplify[1/expr]
$\endgroup$