Hi I am trying to simplify the following expression:$$ \left|\frac{1}{a+ib}\left(\frac{J_1(c x)}{J_1(c b)}-x\right)\right|^2,\quad a,b,x\in \mathbb{R}, \ c\in \mathbb{C} $$ Is there a simple way of simplifying this ? Note, for an arbitrary complex number $z=x+iy$ we can write $$ |z|^2=z\bar z=(x+iy)(x-iy)=x^2+y^2 $$ however, I am not sure how to use that so clearly here because of the Bessel function.
Note, $J_1$ is the Bessel function. Thanks.