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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?

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    [Definition of elementary function](http://www.proofwiki.org/wiki/Definition:Elementary_Function)2012-04-07
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    The definition only lists which functions considered elementary.2012-04-07
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    The 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

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