Is there a theory of transcendental functions? Lately I've been interested in transcendental functions but as I tried to search for books or articles on the theory of transcendental functions, I only obtained irrelevant results (like calculus books or special functions). On the other hand, there's many books and articles on algebraic functions like:


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*Algebraic Function Fields and Codes

*Topics in the Theory of Algebraic Function Fields

*Introduction to Algebraic and Abelian Functions
Are there any references for the theory of transcendental functions? Did anyone studied rigorously such functions or is this field of mathematics outside the reach of contemporary mathematics?

A transcendental function is any function that is not algebraic.  That's about all you can say about them in general.  Of course there are specific classes of transcendental functions that do have interesting theories.
