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maybe the bessel functions are some complicated function of the exponential function, logarithm function... or maybe there's a relation between two or more transcendental functions. Is there a way to prove it?

I was thinking that given two power series (or generalized power series) $f(x)$ and $g(x)$ on the infinite dimensional space of analytic real functions (or even complex), there should be an infinite number of functions $F$ such that $F(f(x),g(x))=0$ so no two transcendental function are independent and the so-called special functions are nothing more than a complicated functions applied to the exponential function for example.

user5402
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  • This is not really a question, is it? I mean it seems that you are expressing in a vague way a belief, which is based solely (right?) on intuition, and then you ask us to back this belief up with an actual proof. Maybe you should try to be less broad and more specific. – Nils Matthes Jun 28 '13 at 20:16
  • for me, giving a name to every new function you use in mathematical physics is like giving a name to every single vector in $\Bbb{R}^3$. I was wondering if anybody had investigated the relationship (not necessarily linear) between special functions. – user5402 Jun 28 '13 at 20:28
  • see http://math.stackexchange.com/questions/9199/what-does-closed-form-solution-usually-mean – graveolensa Jun 29 '13 at 01:27

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