How can I symbolically solve this Bessel function?

I need to solve the following bessel function:

J1(z)=(1/(2*pi*i))*int(exp(i*z*cos(θ))*cos(θ)),θ,0,2*pi),

where z=a*(x+k), a:real, 0<=k,=1.

Could anyone please guide me? It is the first time I deal with a problem like this and I cannot completely figure out what I should do. I need the solution to be a function of x.

Answer 1

[Star Strider]

The best you can likely do is the core MATLAB besselj function.

If you have the Symbolic Math Toolbox, use its besselj function.