Apply Jacobi Anger-Anger expansion and return infinite sum

Source Link

asked Nov 27 at 14:20

Apply Jacobi Anger expansion and return infinite sum

I have an expression

Sin[z Sin[th]]

I want Mathematica to apply the Jacobi Anger expansion, and it works:

FourierTrigSeries[Sin[z Sin[th]], th, 1]

gives 2 BesselJ[1, z] Sin[th]

However, I would like it give the infinite sum

2 Sum[BesselJ[2n-1,z]Sin[(2n-1)th],{n,1,Infinity}]

How should I convince Mathematica to do so?