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Finding the Sum of an Infinite Series

  1. Jun 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the expectation value of the Energy the Old Fashioned way from example 2.2.

    2. Relevant equations

    ##\left< E \right> =\frac { 480\hbar ^{ 2 } }{ \pi ^{ 4 }ma^{ 2 } } \sum _{ odds }^{ \infty }{ \frac { 1 }{ { n }^{ 4 } } } ##

    3. The attempt at a solution
    Never mind the details of the physics problem. I am confident of those bits since it is from an example.

    Using a symbolic math program, how to I only evaluate odds of a summation? I use sage and Wolfram Alpha normally. I tried using sin(pi*n/2)^2 to eliminate the even terms, but neither program seemed to take well to that.

    Thanks,
    Chris
     
  2. jcsd
  3. Jun 25, 2014 #2

    Zondrina

    User Avatar
    Homework Helper

    If I'm reading correctly you only want the sum of the odd terms. So make a change of index. Suppose that ##n = 2k+1##. Then:


    ##\left< E \right> =\frac { 480\hbar ^{ 2 } }{ \pi ^{ 4 }ma^{ 2 } } \sum _{ k=0 }^{ \infty }{ \frac { 1 }{ { (2k+1) }^{ 4 } } } ##
     
  4. Jun 25, 2014 #3
    That might work. Let me give that a shot.

    Chris
     
  5. Jun 25, 2014 #4
    Perfect, thank you.

    Chris
     
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