Re: question

• To: mathgroup at smc.vnet.net
• Subject: [mg74925] Re: question
• From: "Michael Weyrauch" <michael.weyrauch at gmx.de>
• Date: Wed, 11 Apr 2007 02:01:43 -0400 (EDT)
• References: <evd3ku\$5dd\$1@smc.vnet.net>

```Hello,

> In[57]:=
> FullSimplify[Log[x+1],ComplexityFunction\[Rule]
> (Count[{#1},_Log,Infinity]&)]
>

fails, because Log[z] as implemented in Mathematica does not know
the transformation rules back into Hypergeometric functions. If I do it as
follows under Mathematica 5.2 it  works without problems...

Unprotect[Log];

Simplify[Log[x + 1], ComplexityFunction ->
(Count[{#1}, _Log, Infinity] & ),
TransformationFunctions ->
{Log[z_] := Hypergeometric2F1[1, 1, 2, -z + 1]*
(z - 1)}]

(*output*)

x*Hypergeometric2F1[1, 1, 2, -x]

Of course, I have to use Unprotect, since I am adding a rule to an internal command.

So, if for some reason I would like to "simplify" e.g. Log[x+1]^2 it works as exspected

Simplify[Log[x + 1]^2, ComplexityFunction ->
(Count[{#1}, _Log, Infinity] & ),
TransformationFunctions ->
{Log[z_] := Hypergeometric2F1[1, 1, 2, -z + 1]*
(z - 1)}]

(*output*)

x^2*Hypergeometric2F1[1, 1, 2, -x]^2

Therefore, I am not sure, if Andrzej Kozlowski is right here?

Regards   Michael

```

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