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, now the inner sine has an argument which is a product of two variables, and it no longer works:
FourierTrigSeries[Sin[z Sin[a th]], th, 1]
gives
FourierTrigSeries[Sin[z Sin[a th]], th, 1]
How should I convince Mathematica to apply the Jacobi Anger expansion in this case?