What is the meaning of the word TETRACTION as in the sentence " y = x^x is the 2nd order tetraction function" (Math context). Thank You.

Hi symplectyc! The noun "tetraction" is wrong. The correct term is "tetration". Please look at here: http://es.wikipedia.org/wiki/Tetración Bye, Benzene

Thank you very much, Benzene. The paper where I read it said 'tetraction', the wrong spelling. By the way, do you know the propierties of this function, y = x^x ? I just know that is NOT an elementary function. Saludos.

Hi symplectyc! You are right since y = x^x is not an elementary function, but is a particular exponential function. Please look something on it, here: http://www.wolframalpha.com/input/?i=y+=+x^x Bye, Benzene

Hi Benzene! It's not an elementary function, but I think it can be expressed as a combination of elementary ones, just doing: y = x^x <===> y = exp (x log(x)) Nevertheless, f(x) = x^x has not an antiderivative in terms of elementary functions ( I don't know the demonstration of this th.), but the definite integral has not an standard special name, "new special function" (x) = Integral[t^t, 0, x] (say) (Some author calls this "new special function (x)" = Sphd(X), from 'sophomore's dream' (the name given to a pair of identities involving x^x and x^(-x) ) ). Thank you very much for your information, saludos.