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!

Finding the power series expansion of this ln

  1. Jul 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the series expansion of ln(x + sqrt(1+x2))

    2. Relevant equations

    ln(1+x) = x - x2 /2 + x3/3 - x4/4 + ...

    3. The attempt at a solution

    I don't know how to solve this. If it was ln(1+f(x) ) I know I could substitute the x's for f(x) in the ln(1+x) series expansion, but I don't know what to do since the ln isn't in the correct form. Am I supposed to rederive the series from scratch?
     
  2. jcsd
  3. Jul 16, 2012 #2
    Well I solved the whole problem by using the definition of Maclaurin series to find the expansion "from scratch". I used Wolfram Alpha to solve the multiple derivatives necessary, but I'm not satisfied with my answer. I feel like there was a way to solve this by using some kind of substitution, since I managed to solve all the other problems in Mary L Boas book without having to rederive the whole series.

    I'm trying to learn the math tools necessary to self-study undergraduate E&M. I'm an electrical engineering student that would like to know the fundations of my engineering branch :D I feel bad for "cheating" on this problem.
     
  4. Jul 16, 2012 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Hint:

    [tex]ln(x+\sqrt{1+x^2})=ln(x)+ln(1+\frac{\sqrt{1+x^2}}{x})[/tex]
     
  5. Jul 16, 2012 #4
    Wow, I wouldn't have found that by myself. That's a very clever trick, thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook