$$\int_0^t dt_1 \int_0^t dt_2 \int_0^t dt_3 B(t-t_3)F(t_3-t_2) S(t-t_2)F(t_2-t_1)F(t_1) \\ =\int_0^t {dt_2}\, (B*F)(t-t_2)S(t-t_2)(F*F)(t_2) \\ =\big((B*F)S)*(F*F)\big))(t).$$
Iosif Pinelis
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