Perform a Mellin Convolution: New in Wolfram Language 11

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Perform a Mellin Convolution

Perform a Mellin convolution of two functions using MellinConvolve.

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MellinConvolve[UnitBox[x - 3/2], 2 UnitBox[x - 2], x, y]

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Plot the result along with the original functions.

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MellinConvolve[UnitBox[x - 3/2], 2 UnitBox[x - 2], x, y];
Plot[{UnitBox[y - 3/2], 2 UnitBox[y - 2], %} // Evaluate, {y, 0, 6}, 
 Filling -> Axis, Exclusions -> None, PlotRange -> All]

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Perform a Mellin convolution of two Bessel functions.

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MellinConvolve[BesselJ[0, x], BesselJ[1, x], x, y]

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Plot the result along with the original functions.

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MellinConvolve[BesselJ[0, x], BesselJ[1, x], x, y];
Plot[{BesselJ[0, y], BesselJ[1, y], %} // Evaluate, {y, 0, 10}, 
 Filling -> Axis, PlotLegends -> "Expressions"]

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Perform a multivariate Mellin convolution.

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MellinConvolve[3 UnitBox[s - 3/2, t - 7/4], 
 2 UnitBox[s - 1, t - 1], {s, t}, {m, n}]

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Plot the result along with the original functions.

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MellinConvolve[3 UnitBox[s - 3/2, t - 7/4], 
 2 UnitBox[s - 1, t - 1], {s, t}, {m, n}];
Plot3D[{3 UnitBox[m - 3/2, n - 7/4], 2 UnitBox[m - 1, n - 1], %} // 
  Evaluate, {m, 0, 3}, {n, 0, 3}, PlotRange -> All, Filling -> Axis, 
 PlotPoints -> 50, Exclusions -> None, PlotStyle -> Opacity[0.4], 
 Ticks -> None, Mesh -> None]

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