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

Maclaurin series of an elementary function question

  1. Nov 2, 2013 #1
    The Maclaurin series expansion for ##(1+z)^\alpha## is as follows:

    $$(1+z)^\alpha = 1 + \sum_{n=0}^\infty \binom{\alpha}{n}z^n$$ with $$|z|<1$$


    What I don't understand is why is ##|z|<1##?
     
  2. jcsd
  3. Nov 2, 2013 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The series won't converge for α, unless α is a non-negative integer.
    The magnitude of the binomial coefficient -> 1 as n -> ∞.
     
    Last edited: Nov 2, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Maclaurin series of an elementary function question
  1. Question on functions (Replies: 5)

Loading...