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As we know, the integral may convert or map a rational function or algebraic function into a transcendental one. Are there any other operators that may convert a rational function or algebraic function into transcendental one?

Further, are there any other operators that may convert transcendental function into algebraic or rational one like the derivative?

Those operators that are computable are most welcome.

Any reference is welcome. Review of such operators are most welcome.

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  • $\begingroup$ What is your definition of transcendency? $\endgroup$ Jul 22, 2014 at 13:38
  • $\begingroup$ @O.L. the functions defined over complex number that satisifies algebraic equation are algebraic,otherwise are transcendental $\endgroup$ Jul 22, 2014 at 13:40
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    $\begingroup$ Then $\exp$, $\ln$ or the operation of taking the inverse function fit your queries. $\endgroup$ Jul 22, 2014 at 13:46
  • $\begingroup$ What does this question have to do with functional analysis or several complex variables? $\endgroup$
    – mrf
    Jul 22, 2014 at 15:01

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