The simplify/wronskian function is used to simplify expressions that contain the subexpression $fg\'-gf\'$, denoted $\mathrm{wr}\left(f\,g\right)$, with f and g special functions.  In particular, it recognizes the wronskians of

* Identical functions whose indices sum to zero, for example, $\mathrm{wr}\left(J\left(v\,z\right)\,J\left(-v\,z\right)\right)$

* Two functions with the same indices, for example, $\mathrm{wr}\left(J\left(v\,z\right)\,Y\left(v\,z\right)\right)$

* A function with arguments that sum to zero, for example, $\mathrm{wr}\left(\mathrm{D}\left(v\,z\right)\,\mathrm{D}\left(v\,-z\right)\right)$

$\mathrm{simplify}\left(\mathrm{BesselJ}\left(v+1\,z\right)\mathrm{BesselJ}\left(-v\,z\right)+\mathrm{BesselJ}\left(v\,z\right)\mathrm{BesselJ}\left(-v-1\,z\right)\,\mathrm{wronskian}\right)$

$-\frac{2\sin \left(v\mathrm{\pi }\right)}{\mathrm{\pi }z}$

$\mathrm{simplify}\left(\mathrm{BesselJ}\left(v+1\,z\right)\mathrm{BesselY}\left(v\,z\right)-\mathrm{BesselJ}\left(v\,z\right)\mathrm{BesselY}\left(v+1\,z\right)\,\mathrm{wronskian}\right)$

$\frac{2}{\mathrm{\pi }z}$