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Perturbation theory and asymptotics

  1. Oct 28, 2010 #1
    I need to find the roots of the transcendental function,


    I've done many problems like this before and am fairly sure this is just a regular perturbation problem. The difficulty I'm having is with the exponential term.

    Could anyone give me an idea of how to tackle this problem?

  2. jcsd
  3. Oct 29, 2010 #2


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    Science Advisor

    Approximate the exponential with a Taylor's polynomial:
    [tex]exp(-x/a)= 1- x/a+ \frac{x^2}{2a^2}+ \cdot\cdot\cdot+ (-1)^n\frac{x^n}{n!a^n}[/tex]
  4. Oct 29, 2010 #3
    Sorry I didn't make it clear in my first post, I'm finding the roots of the equation as a tends to 0. I thought about the Taylor expansion but then the terms are being divided by 0 (as a tends to zero). Is there anyway around this?

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