the translation operator associated with the Bessel operator

Question

the translation operator associated with the Bessel operator is given by: $$\tau_x^{\nu} f(y) = \frac{\Gamma(\nu+1)}{\sqrt{\pi}\Gamma\left(\nu+\frac{1}{2}\right)} \int_{0}^\pi f\left(\sqrt{x^2+ y^2-2 xy\cos(\theta) }\right)(\sin(\theta))^{2v} \,d\theta.$$ Show that there exists a function $W(x,y,.)$ s.t $$\tau_x^{\nu} f(y)=\int^{\infty}_{0}f(t)W(x,y,.)d\mu$$ where $d\mu(x)=\frac{x^{2v+1}}{2^v \Gamma(v+1)}dx.$ Any hints please.