XPost: sci.math   
   From: ivgroups@onlinehome.de   
      
   I am interested here in *symbolically* given functions, that means in   
   expressions of some Special functions (Named functions) (Wikipedia: Special   
   functions), e.g. the Elementary functions (Wikipedia: Elementary function).   
   Let all be in the Real numbers or in the Complex numbers. Let the domains of   
   the functions unconsidered.   
   When (under what conditions) is the inverse of a symbolically given function   
   also a function which can be represented symbolically?   
      
   At least partial solutions can be derived.   
      
   Liouville's theorem (Wikipedia: Liouville's theorem (differential algebra))   
   give an answer for the antiderivative of a symbolically given function.   
      
   I think, the answers to this mathematical problem have important   
   applications in mathematics, and in some other non-mathematical usages -   
   usages with importance / with impact to the real life.   
      
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