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

Non-convergent power series but good approximation?

  1. Dec 11, 2011 #1
    Hello,

    In my QM class we're using power series which don't converge but apparently still give a good approximation if one only takes the lower-order terms.

    Is there any way to understand such a phenomenon? Is it a genuine area of mathematics? Or is it impossible to say something general on this phenomenon?
     
  2. jcsd
  3. Dec 11, 2011 #2
    ^ Power series are just polynomials, right? So essentially you're approximating using low-order polynomials. I don't know anything about QM but that'd be my guess as to why what you're doing is reasonable.
     
  4. Dec 11, 2011 #3

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    It might help to look at the math for a particular series to see what is going on. For example http://en.wikipedia.org/wiki/Stirling's_approximation

    Usually, the terms of the divergent series reduce in size to a minimum and then increase. If you take the sum up to the smallest term in the series, the relatve error, | approximate value - exact value | / exact value, may converge to 0, even though the absolute error | approximate value - exact value | diverges.
     
  5. Dec 11, 2011 #4
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Non-convergent power series but good approximation?
  1. Power Series (Replies: 2)

  2. Convergence of Series (Replies: 17)

  3. Convergent Series (Replies: 3)

Loading...