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Math Help - Transcendental exponential equation

  1. #1
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    Transcendental exponential equation

    I believe this equation to transcendental wrt x, does anyone have any tips for solving/evaluating it, i.e. analytic continuation etc!!

    Ae^{-ikx} + Be^{-imx} + Ce^{-i2kx} + De^{-i2mx} + Ee^{-i(k+m)x} + F = 0

    where A-F are real, and m,k real.
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  2. #2
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    Re: Transcendental exponential equation

    Hey TomGibbons.

    Can you use formulas to inductively contract the term to a single term of sines and cosines?

    en.wikipedia.org/wiki/List_of_trigonometric_identities

    The idea is to reduce it to some kind of real and complex part by continually reducing terms by using the identities to get a final answer. It's just a thought, don't know if it will be useful.
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