# tetraction

Discussion in 'Specialized Terminology' started by symplectyc, Jun 27, 2013.

1. ### symplectycNew Member

spanish
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.

2. ### BenzeneSenior Member

GENOA (ITALY)
Italian from Italy
3. ### symplectycNew Member

spanish
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.

4. ### BenzeneSenior Member

GENOA (ITALY)
Italian from Italy
5. ### symplectycNew Member

spanish
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.

6. ### BenzeneSenior Member

GENOA (ITALY)
Italian from Italy
If we continue to discuss about Math we will be banned surely!

Bye,

Benzene

7. ### symplectycNew Member

spanish
Hi Benzene!

OK, and thanks for all your information,

symplecty