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simplify/wronskian

simplify expressions involving wronskian identities

 Calling Sequence simplify(expr, wronskian)

Parameters

 expr - any expression wronskian - literal name; wronskian

Description

 • 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, $\mathrm{wr}\left(\mathrm{D}\left(v,z\right),\mathrm{D}\left(v,-z\right)\right)$

Examples

 > $\mathrm{simplify}\left(\mathrm{BesselJ}\left(v+1,z\right)\mathrm{BesselJ}\left(-v,z\right)+\mathrm{BesselJ}\left(v,z\right)\mathrm{BesselJ}\left(-v-1,z\right),\mathrm{wronskian}\right)$
 ${-}\frac{{2}{}{\mathrm{sin}}{}\left({v}{}{\mathrm{\pi }}\right)}{{\mathrm{\pi }}{}{z}}$ (1)
 > $\mathrm{simplify}\left(\mathrm{BesselJ}\left(v+1,z\right)\mathrm{BesselY}\left(v,z\right)-\mathrm{BesselJ}\left(v,z\right)\mathrm{BesselY}\left(v+1,z\right),\mathrm{wronskian}\right)$
 $\frac{{2}}{{\mathrm{\pi }}{}{z}}$ (2)