Impossible expressions

  • #1
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I've heard it is possible to prove, that some functions, for example defined with integral expressions, cannot be written with elementary functions (in somehow finite manner). Since I don't have a clue of how these things are proven, I'm now merely asking, that what kind of proofs these proofs are? What are they based on?

Since the problem setting seems similar to that of solving quintic, I must ask, does this thing have anything to do with Galois theory? I mean, could this be a reason to start studying it?

(I'm not sure wheter this belongs under analysis or algebra or logic or what...)
 
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  • #3
Funny how I never happened to hit the words "differential" and "galois" into the google at the same time :rolleyes:
 
  • #4
If you can find Watson's Theory of Bessel Functions, then you will run into many pages of proofs and discussions of whether certain differential equations can be solved in terms of elementary functions. Tricky and tough.

Regards,
Reilly Atkinson
 

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