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

A weird expansion

  1. May 3, 2010 #1
    Dos this fractional Taylor series

    [tex] (a+x)^{-r} = \sum_{m=-\infty}^{\infty} \frac{ \Gamma (-r+1)}{\Gamma (m+\alpha+1) \Gamma(-r-n-\alpha+1)}a^{(-r-m-\alpha )}x^{m+\alpha} [/tex]

    makes sense for x < 1 or x >1 and alpha being an arbitrary real number ..for example ?? , here a and r are real numbers , the idea here is if we can define a fractional power series expansion generalizing the usuarl Laurent or Taylor series.
  2. jcsd
  3. May 5, 2010 #2
    I tried [itex]r= 1,\alpha=1/2,a=1,x=1/2[/itex].
    The series diverges since the term does not go to zero as [itex]m \to -\infty[/itex]

    P.S. You have misprint [itex]n[/itex] for [itex]m[/itex] , right?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - weird expansion Date
I Taylor expansion of f(x+a) Nov 1, 2017
I Some weird circular relationship Jun 17, 2016
1+2+3+4+...=-1/12 weirdness Jun 5, 2015
Weird integral - what's wrong? May 17, 2015
Weird idea (gradients and potentials) Aug 31, 2014