Hey there Sign in to join this conversationNew here? Join for free

Radius of convergence and Frobenius method

Announcements Posted on
Study Help needs new mods! 14-04-2014
Post on TSR and win a prize! Find out more... 10-04-2014
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    I am solving a differential equation using the Frobenius method, however halfway through, I have introduced a new power series. I have been told that I need to show the radius of convergence of this series. Why would I have to do that?
    • 3 followers
    Offline

    (Original post by claret_n_blue)
    I am solving a differential equation using the Frobenius method, however halfway through, I have introduced a new power series. I have been told that I need to show the radius of convergence of this series. Why would I have to do that?
    So that you know when it converges :p: For instance, if you introduced a power series whose radius of convergence is zero, your solution isn't going to be of much use.

    Without knowing more details I can't give you much more of a helpful answer than this!
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    (Original post by nuodai)
    So that you know when it converges :p: For instance, if you introduced a power series whose radius of convergence is zero, your solution isn't going to be of much use.

    Without knowing more details I can't give you much more of a helpful answer than this!
    It's that same differential equation I've been working on for the past, what, 2 weeks? 3 weeks?

    I still can't seem to solve it.

    This was just because I got told that I needed to make a point about the radius of convergence.

    Seeing as your online, please could you help me wit it.I am really stuck on one bit about solving DE's using Frobenius. I have a recurrance relation as:

      \frac{h^2}{2m}(\lambda)(\lambda + 1)b_{\lambda+2}  -A b_{\lambda + 1} + (E - Aa)b_{\lambda } = 0

    Where h , A < 0 and a and E are constants. How do I solve this from here? I can solve DE's using power series if there are two "unkowns" but how do I do it using three?

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

  2. Slide the button to the right to create your account

    Slide to join now Processing…

    You don't slide that way? No problem.

Updated: May 3, 2012
Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.