Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Series expansions of log()

  1. Feb 18, 2017 #1
    Hi,

    see attached PdF file for my question concerning serie expansion of log(z) at infinity.

    Thank you
    Belgium 12
     

    Attached Files:

  2. jcsd
  3. Feb 18, 2017 #2

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    So the usual expansion for [itex]log(1+x)[/itex] when [itex]x[/itex] is small is given by:

    [itex]log(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - ...[/itex]

    We also know that [itex]log(1+z) = log(z (1 + \frac{1}{z})) = log(z) + log(1 + \frac{1}{z})[/itex]

    So you can put the two together (replacing [itex]x[/itex] by [itex]\frac{1}{z}[/itex]):

    [itex]log(1+z) = log(z) + \frac{1}{z} - \frac{1}{2 z^2} + \frac{1}{3 z^3} ...[/itex]​
     
  4. Feb 18, 2017 #3

    Mark44

    Staff: Mentor

    Instead of posting an image of barely legible writing, please learn to use LaTeX. Everything you wrote can be entered directly into the input pane here. See our tutorial on LaTeX here: https://www.physicsforums.com/help/latexhelp/

    Here are some examples of expressions you wrote and how they appear in LaTeX:
    ##\log(\frac{z - 1}{z})##
    Script for the above: ##\log(\frac{z - 1}{z})##

    $$\sum_{q \ge 1}^{\infty} \frac{(-1)^q}{qz^q}$$
    Script for the above: $$\sum_{q \ge 1}^{\infty} \frac{(-1)^q}{qz^q}$$

    (Inline version of the above would be ##\sum_{q \ge 1}^{\infty} \frac{(-1)^q}{qz^q} ##.)


    BTW, in the summation that appears twice, it's very difficult to tell that the denominator is ##qz^q##. What you wrote--twice--looks like ##qzq##. The only clue that the exponent is q is that this letter appears slightly raised.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Series expansions of log()
  1. Series expansion (Replies: 4)

  2. Expansion of log(1+x) (Replies: 5)

  3. Log expansion (Replies: 1)

  4. Series expansion (Replies: 1)

Loading...