Question Number 219579 by SdC355 last updated on 29/Apr/25
$$\int_{\mathrm{0}} ^{\:\infty} \:\:\mathrm{sin}\left({t}\right){J}_{\nu} \left({kt}\right)\:\mathrm{d}{t} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:{t}\centerdot{J}_{\nu} \left({at}\right){J}_{\nu} \left({kt}\right)\:\mathrm{d}{t} \\ $$