1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Taylor Series Expansion for the Relativistic Factor of Momentum

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Using the technique of Taylor expansion, find an approximate expression for the relativistic factor γ for small v (i.e., expanded around v = 0) that is correct to order v2.

    2. Relevant equations
    γ=1/SQRT(1+ V2/C2). But in class, my professor just substituted X=V/C, so the equation became γ=1/SQRT(1-X2).

    3. The attempt at a solution
    I tried to expand the function γ(v) with v at 0.....
    However, this expression wasn't correct. I'm not really sure how else to expand it! Any help would be much, much appreciated, thanks!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 26, 2010 #2


    Staff: Mentor

    With that substitution, you get y = 1/sqrt(1 + x2).
    This is really y(x) with x at 0. If v = 0, then x = 0. It's very likely that the sign error above is affecting what you got for your Maclaurin series.
  4. Jan 26, 2010 #3
    Sorry for that typo! The actual function is y=1/SQRT(1-V2/C2).

    In finding the parts of this maclaurin series, I have...

    Sorry for my lack of showing my work, but I believe those expressions are right
    when using the yn(v)=[f(n)(X0(X-X0)n]/n!
  5. Jan 26, 2010 #4
    how to Put the Boolean function q'r + p'q' + pq'r' into DNF and find a simpler representation for the function using a Karnaugh map. Show the output of this simpler function is the same as in question 1 for p = 1, q = 1, r = 0.
  6. Jan 26, 2010 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Your derivatives are wrong because you're mixing in stuff from the series expansion. You should have:

    [tex]y(X)=1/\sqrt{1-X^2} \rightarrow y(0)=1[/tex]
    [tex]y'(X)=X/(1-X^2)^{-3/2} \rightarrow y'(0)=0[/tex]

    and so on. You then plug these values for y(0), y'(0), y''(0) into the series expansion.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook