Why exponentiation and power function with non-integer power are considered elementary functions while some other functions like Bernoulli polynomials generalized to non-integer order, polylogarithm, Hurwitz zeta and polygamma are not?
Why exponentiation is considered elementary funtion?
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$\begingroup$
special-functions
gamma-function
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0[Definition of elementary function](http://www.proofwiki.org/wiki/Definition:Elementary_Function) – 2012-04-07
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0The definition only lists which functions considered elementary. – 2012-04-07
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3The definition is rather arbitrary, and dictated by history. I think only a historian of mathematics can give a better answer than this, and it will probably come down to the same answer, just in more words. – 2012-04-07