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1

You could also use: cm[f_, s_, t_, n_] := InverseLaplaceTransform[LaplaceTransform[f, s, t]^(n + 1), t, s] (s>0): e.g. TableForm[Table[{j, cm[Exp[-a s] UnitStep[s], s, t, j]}, {j, 1, 10}], TableHeadings -> {None, {"n", "n-fold Convolution"}}]

0

Thanks to all who helped or tried to help me here, finally I found a solution. My special function was the exponential distribution but one can apply it for any arbitrary function. f[x_] = \[Lambda]*Exp[-\[Lambda]*x] UnitStep[x]; g[x_] = \[Lambda]*Exp[-\[Lambda]*x] UnitStep[x]; convi[n_] := {Do[ g[x[i]] = Convolve[f[x[i - 1]], g[x[i - 1]], x[i - 1], ...

4

This is a bug in DiscreteConvolve[]. The bug is caused by a missing condition (m>=0) in one term of the answer returned by DiscreteConvolve[] for your example. A workaround for the problem is to apply PiecewiseExpand[] to the first two arguments of DiscreteConvolve[] as shown below. h = (1/2)^n UnitStep[n] - 3*(1/2)^(n - 1) UnitStep[n - 1]; g = 3^n ...

0

Perhaps this suffices: f[x_, y_] := NIntegrate[ UnitBox[s, t] BesselK[0, Sqrt[(x - s)^2 + (y - s)^2]], {s, -Infinity, Infinity}, {t, -Infinity, Infinity}] Visualizing: Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, PlotRange -> Full, Mesh -> False, PlotPoints -> 25] Plot could be improved but I do not have time at present.

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