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A general Series sum.

  1. Dec 20, 2009 #1


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    usually in analysis we are dealing with power series, my question is there coverage of a general series with exponent is any real function of n natural.
    i.e something like this:
    [tex]\sum_n a_n x^{b_n}[/tex]
    where b_n is some real function of n.

    Thanks in advance.
  2. jcsd
  3. Dec 20, 2009 #2


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    I am not sure what your question is. Certainly one can have a series like that but it is not a power series and would not, in general, have the nice properties, radius of convergence, etc., of power series. I suspect you could show similar properties for specific sequence [math]b_n[/math] but they would then be as restrictive as power series.
  4. Dec 20, 2009 #3


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    I guess I am looking for something dealing with the most general case of a series such as this one, if something like this exists.
    obviously a radius of convergence like in power series is not guarnteed, but perhaps something else?
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