Re: FullSimplify on Gamma functions

• To: mathgroup at smc.vnet.net
• Subject: [mg48115] Re: [mg48099] FullSimplify on Gamma functions
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 14 May 2004 00:12:16 -0400 (EDT)
• References: <200405130408.AAA26697@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 13 May 2004, at 13:08, Oleksandr Pavlyk wrote:

> Dear group,
>
> Consider
>
> In[1]:=
> a[m_]:=(q1)^m * Gamma[q2]/Gamma[2*m+q3];
>
> Then
>
> In[2]:=
> FullSimplify[a[m-1]/a[m]]
>
> simplifies ratio of gamma functions just fine.
> However
>
> In[3]:=
> FullSimplify[ a[m+1]/a[m] ]
>
> fails to do so, leaving the ratio untouched.
>
> FullSimplify[ (a[m+1]/a[m])^(-1) ]^(-1)
>
> gives me what I expect.
>
> I've been trying to assist FullSimplify with
>
>
> to no avail. I would appreciate anybody illuminating
> me on how to extend FullSimplify to handle this case.
>
> Thank you in advance,
> Sasha
>
>
The problem is indeed wiht ComplexityFunction. You need to find one for
which the answer you want has a lower value (LeafCOunt gives the same
value of 17 for both the answer you get and the one you want). One
thing that works is Depth:

FullSimplify[a[m + 1]/a[m], ComplexityFunction -> Depth]

q1/((2*m + q3)*(1 + 2*m + q3))

You can also use a customized funciton, just for this case:

f[x_] := Count[x, Gamma, Infinity, Heads -> True]

FullSimplify[a[m + 1]/a[m], ComplexityFunction -> f]

q1/((2*m + q3)*(1 + 2*m + q3))

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

```

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