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Math Help - Integral involving Bessel Function

  1. #1
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    Integral involving Bessel Function

    Hi I have a question regarding this integral. I was wondering if someone here can help. Thanks.

    Question: Evaluate \int_0^\infty\frac{xJ_0(x)}{\sqrt{a^2+x^2}}dx
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  2. #2
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    Quote Originally Posted by nonsingular View Post
    Hi I have a question regarding this integral. I was wondering if someone here can help. Thanks.

    Question: Evaluate \int_0^\infty\frac{xJ_0(x)}{\sqrt{a^2+x^2}}dx
    The solution to this and the other one is one of the most beautiful integrations I have ever seen and wish it not go unnoticed over here:

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