Does someone know the solution (simple closed form) of one of theses integrals: $$\int_0^t J_l(s) e^{-iA(t-s)}ds$$ $$\int_0^t \frac{J_l(s)}{s} e^{-iA(t-s)}ds$$ with $l>0$, $t>0$, $\Re(A)>0$, $\Im(A)<0$.
Thank you very much.
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$\begingroup$ ? solution ? I don't see much reason to hope for some simple closed form expression. $\endgroup$– Carlo BeenakkerCommented Jul 5, 2014 at 13:57
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$\begingroup$ Can you do this special case? $$\int _{0}^{t}\!{{\rm J}_1(s)}{{\rm e}^{-2\,i ( t-s ) }}{ds} $$ $\endgroup$– Gerald EdgarCommented Jul 5, 2014 at 15:27
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