Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A general Series sum.

  1. Dec 20, 2009 #1

    MathematicalPhysicist

    User Avatar
    Gold Member

    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

    HallsofIvy

    User Avatar
    Science Advisor

    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

    MathematicalPhysicist

    User Avatar
    Gold Member

    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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook