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Math Help - integral bessel function

  1. #1
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    integral bessel function

    Dear members,

    I have a problem with the summation for computing this integral.(see attached pdf file)

    I downloaded it from the intenet.

    My problem is shown on the pdf file.

    Thank you
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  2. #2
    MHF Contributor
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    Re: integral bessel function

    Hey Gilbert.

    Hint: Try going from x^(2n+2)/(2n+2)! * (-1)^n to x^(2n)/(2n)!*(-1)^n by changing the limits n=0 to infinity to n=1 to infinity and then use the fact that:

    cos(x) = 1 - Sigma(n=1) x^(2n)/(2n)! * (-1)^n which implies

    Sigma(n=1) x^(2n)/(2n)! * (-1)^n = 1 - cos(x)
    Thanks from mopen80
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