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Criticism about resummation methods.

  1. May 26, 2007 #1


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    I have been studying the 'resummation' methods for divergent series..however i have some questions of critcs.


    Yes Borel method is very beatiful however ..can you get for every sequence of a(n) so [tex] \sum_{n=0}^{\infty} a_{n} [/tex] is divergent, the value of:

    [tex] \sum_{n=0}^{\infty} a_{n}\frac{x^{n}}{n!} =f(x) [/tex] ??


    You have the same problem, for example for 'lambda' big you will never be able to give a value for expressions like:

    [tex] \sum_{n \le \lambda}(1- \frac{n}{\lambda})^{\delta} \Lambda (n) [/tex]


    Hence, my opinion is that if we can only use this resummation method for only a few cases are they still useful ?? (i'm not saying these methods are WORNG but perhaps they are completely 'useless' )
  2. jcsd
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