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Math Help - Any help on this definite integral ?

  1. #1
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    Any help on this definite integral ?

    Any ideas on how to tackle this integral ?


    \int_{-1}^{1} dt \cos(a t) \cos (b \sqrt{1-t^{2}})

    I know that the 'sine' version can be solved in terms of a Bessel function (Gradstein 3.711):

    \int_{-1}^{1} dt \cos(b t) \sin (a \sqrt{1-t^{2}}) = -\pi \frac{\partial}{\partial a} J_{0}(\sqrt{a^2 + b^2})
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  2. #2
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    Re: Any help on this definite integral ?

    Hey quique.

    Have you seen this identities before? They might help.

    List of trigonometric identities - Wikipedia, the free encyclopedia
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