question

*To*: mathgroup at smc.vnet.net*Subject*: [mg74865] question*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Mon, 9 Apr 2007 06:11:15 -0400 (EDT)

BesselI[n, x] can be expressed as (x^n*Hypergeometric0F1Regularized[1 + n, x^2/4])/2^n Mathematica knows this and simplifies the hypergeometric function (applying FunctionExpand or FullSimplify) In[53]:= (x^n*Hypergeometric0F1Regularized[1 + n, x^2/4])/2^n//FunctionExpand Out[53]= BesselI[n, x] The opposite is also possible. In[54]:= FullSimplify[BesselI[n, x], ComplexityFunction -> (Count[{#1}, _BesselI, Infinity] & )] Out[54]= (x^n*Hypergeometric0F1Regularized[1 + n, x^2/4])/2^n The same holds true for some special functions I have tried. Let see a more trivial function: Log[1+x]. Log[1+z] can be expressed as z*Hypergeometric2F1[1, 1, 2, -z] and Mathematica automatically simplifies the hypergeometric series In[55]:= z*Hypergeometric2F1[1, 1, 2, -z] Out[55]= Log[1 + z] Is it possible the opposite through some command(s)? Something like the following does not look very smart. That's why it fails! In[57]:= FullSimplify[Log[x+1],ComplexityFunction\[Rule] (Count[{#1},_Log,Infinity]&)] Out[57]= Log[1+x] Thanks Dimitris

**Follow-Ups**:**Re: question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>