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What is the summation formula?

  1. Oct 2, 2004 #1
    What would be the sum formula for the summation in the attachment?

    For any real constant 'c', what is the sum formula for

    sigma (n^c) ?

    Attached Files:

  2. jcsd
  3. Oct 4, 2004 #2
    oh sorry! :frown: the file needs mathtype to view....sorry!

    This file is GIF image format--should be easier to open i hope :surprised
    I attached the equation as a GIF image file...i hope it can be open....the GIF file that i attached (the equation is a GIF image file...yeah) (whtisthsum.gif)

    (*Note: this is not really a power series--the exponent 'c' is a constant!! does not change!...so the sum really goes like

    The exponent c does not change...it is the same for every term of the equation as u add them up...(2^c) and so on to (k^c)..the c exponent does not change, so it's not really a power series)

    Attached Files:

    Last edited: Oct 4, 2004
  4. Oct 4, 2004 #3


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    I don't believe there's a general closed form for that sum

    There are formulas for specific whole number value of c. ie : for c=0,1,2,3 etc.

    Also, it's not hard to find a formula, for a general positive integer value of c. This can be done by simply assuming the sum is a polynomial of degree c+1, and determining the coefficients by plugging in the first c+2 values of the sum.

    Need to think more about a general method for real c.
  5. Oct 4, 2004 #4


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    Of course, that's other than using Mathematica, or Maple. In fact, this can be done quite easily using Excel, too.
  6. Oct 5, 2004 #5
    Wait, but what would the formula be for any real c>0 ?

    I tried solving it, but is there a formula for (a+b)^c , where c>0 but where 'c' could be real???...(not just natural). Let's just take the case where (a+b)>0 , because u cannot have a real root for an irrational power of a negative number...

    So is there a formula for (a+b)^c where c is real and c>0 and (a+b)>0?

    Look at the attachments...um, i posted three sorry :frown:
    I needed to break one GIF file into two...so there are three (sorry)

    Attached Files:

  7. Oct 5, 2004 #6


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    I don't believe there is a general formula for real c. If you use the binomial expansion for [itex](a+b)^c~,~c~\epsilon~\mathbb{R}[/itex], you will still have terms like [itex]a^c[/itex].

    You don't have to be including attachments for math representations. You can simply use LaTeX typesetting, as I've done. Look at this thread for LaTeX :
  8. Oct 8, 2004 #7
    Hmm...i've found a solution elsewhere on some polysum tripod site:

    < http://polysum.tripod.com/ >

    What does it mean when an integrand is written only with a lower limit without an upper one?
    Does that mean it applies from that lower limit to infinity? or something else?
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