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Math Help - calculating a series

  1. #1
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    iran
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    Post calculating a series

    Hi,

    I'm trying to calculate this series!

    calculating a series-untitled.png

    a and b are two constants.

    is there any answer for this series??

    Any Answer is helpful.

    hasti
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  2. #2
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    Re: calculating a series

    Well, seeing as b is a constant, that implies that as m goes through the different values, from one to infinity, b is unaffected. So, what can we do with it?


    EDIT: If it isn't immediately evident why b remains unaffected as m goes through its different values, and what we can do with it, let's calculate a partial sum of this series. Let's find the sum for just m=1,2,~and~3

    \frac{e^{-a \cdot (1)^2}}{b \cdot (1)^2} + \frac{e^{-a \cdot (2)^2}}{b \cdot (2)^2} + \frac{e^{-a \cdot (3)^2}}{b \cdot (3)^2}

    What do you notice about "a" and "b," as m goes from 1 to 3?
    Last edited by Bashyboy; February 24th 2013 at 03:42 AM.
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  3. #3
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    Re: calculating a series

    I edited my post, hasti.

    EDIT: Actually, I don't know how helpful it will be. I misread what sort of series you have.
    Last edited by Bashyboy; February 24th 2013 at 03:45 AM.
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  4. #4
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    Re: calculating a series

    Yes, It's correct. Then now, We should calculate this series when b is eliminated!

    But i don't know how to do it!

    calculating a series-untitled1.png
    Attached Thumbnails Attached Thumbnails calculating a series-untitled.png  
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  5. #5
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    Re: calculating a series

    Well, b isn't eliminated, it's just factored out of the series. Are you sure there isn't suppose to be an addition sign between a and m^2?
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  6. #6
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    iran
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    Re: calculating a series

    let me to explain with an example!
    we know that
    calculating a series-untitled2.png
    now i should find an equivalent for
    calculating a series-untitled1.png

    thanks
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  7. #7
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    iran
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    Re: calculating a series

    we don't need any extra sign between a and m^2. a is a coefficient for m^2 and (a*m^2) is a power for e.

    thanks for your attention.
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