This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 FunctionExpand FunctionExpand[ expr ] tries to expand out special functions in expr, when possible reducing compound arguments to simpler ones. FunctionExpand uses a large collection of rules. FunctionExpand is automatically called by FullSimplify. See the Mathematica book: Section 3.2.13. See also: TrigExpand, TrigToExp, ComplexExpand, FullSimplify. Further Examples Here is an elementary simplification. In[1]:= Out[1]= The incomplete gamma function with an integer as the first argument is expressible in terms of exponentials. In[2]:= Out[2]= The next few examples yield results that still contain special functions, but are considered simpler by Mathematica because the arguments of the resulting special functions are simpler. In[3]:= Out[3]= In[4]:= Out[4]= In[5]:= Out[5]= FunctionExpand acts like PowerExpand when appropriate. In[6]:= Out[6]= Here FunctionExpand refrains from distributing the exponent, since and are not always equal. In[7]:= Out[7]= In[8]:= Out[8]= In[9]:= Out[9]= A common use of FunctionExpand is to simplify trigonometric expressions involving integer or half-integer multiples of the arc. In[10]:= Out[10]= In[11]:= Out[11]= Many functions can be expressed in terms of gamma functions. In[12]:= Out[12]= This can be convenient in checking identities. In[13]:= Out[13]= Here are some other examples where FunctionExpand expresses exotic or specialized functions in terms of more familiar or more fundamental ones. In[14]:= Out[14]= In[15]:= Out[15]= In[16]:= Out[16]=