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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?

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  • $\begingroup$ You must solve integral : $$\frac{\int_{-\pi }^{\pi } \sin (z \sin (a t)) \sin (t) \, dt}{\pi }$$ ? I doubt there's a closed-form for integral. I have solution expressed by complicated infinty series with 2F1 hypergeometric function. $\endgroup$ Commented Nov 27 at 16:35
  • $\begingroup$ Some rudeness on here it seems. $\endgroup$
    – ngc5139
    Commented Nov 27 at 17:43

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