# Any help on this definite integral ?

• November 21st 2012, 07:45 AM
quique
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):

$\int_{-1}^{1} dt \cos(b t) \sin (a \sqrt{1-t^{2}}) = -\pi \frac{\partial}{\partial a} J_{0}(\sqrt{a^2 + b^2})$
• November 21st 2012, 09:17 PM
chiro
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