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An inversion theorem for Laplace-Stieltjes transforms

An inversion theorem for Laplace-Stieltjes transforms

showed that under certain assumptions of boundedness for F(x), lim (V(τ)[l -exp ( -e"-^8)] dτ = Γ F{τ)dτ . S-> + ooJθ JOIf we write 1 -exp(e s{t ~τ) ) = ΣΓ(-l) w+1 c nx{t ^\n\ in the above formula, and interchange sum and integral, we formally obtain lim = …