tetraction

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

  1. symplectyc New 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. Benzene

    Benzene Senior Member

    GENOA (ITALY)
    Italian, Italy
  3. symplectyc New 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. Benzene

    Benzene Senior Member

    GENOA (ITALY)
    Italian, Italy
  5. symplectyc New 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. Benzene

    Benzene Senior Member

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

    Bye,

    Benzene
     
  7. symplectyc New Member

    spanish
    Hi Benzene!

    OK, and thanks for all your information,

    symplecty
     

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