1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series Soln to a Diff Eqn: can't understand one of the steps

  1. Aug 11, 2015 #1
    1. The problem statement, all variables and given/known data

    solve y" - 2xy' + y = 0

    2. Relevant equations


    3. The attempt at a solution

    in the worked example, the book gets from

    here:

    [tex]\sum\limits_{n=0}^{\infty} (n+1)(n+2)c_{n+2}x^n - \sum\limits_{n=1}^{\infty}2nc_nx^n + \sum\limits_{n=0}^{\infty}c_nx^n = 0[/tex]

    to here:

    [tex] \sum\limits_{n=0}^{\infty} [(n+1)(n+2)c_{n+2} - (2n-1)c_n]x^n = 0[/tex]

    by way of:

    [tex]\sum\limits_{n=1}^{\infty}2nc_nx^n = \sum\limits_{n=0}^{\infty}2nc_nx^n[/tex]

    How is this last part justified?
     
  2. jcsd
  3. Aug 11, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    What is the value of ##2nc_nx^n## when ##n=0##?
     
  4. Aug 11, 2015 #3
    I considered that. It's zero. But assuming [itex]c_n[/itex] exists, won't [itex]2nc_nx^n \neq 0 \ for \ n=1[/itex]?
     
  5. Aug 11, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes, but that is irrelevant. The two sums differ by the presence/absence of the ##n = 0## term, which is zero!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted