gives the Mellin convolution with respect to x of the expressions f and g.
gives the multidimensional Mellin convolution.
Details and Options
- The Mellin convolution of two functions and is given by .
- The multidimensional Mellin convolution of two functions and is given by .
- The following options can be given:
Assumptions $Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic method to use
Examplesopen allclose all
Basic Uses (3)
Compute the PDF for the product of two random variables:
MellinConvolve gives the PDF for the product of these random variables:
Compare with the result from TransformedDistribution:
The integral depends on the parameter α. Find the value of α that lies between 0 and 5 and maximizes the integral. The given integral can be regarded as a Mellin convolution of two functions:
Compute the Mellin convolution of f[x] and g[x]:
Compare with the result given by Integrate:
Plot the integral as a function of α:
Compute the argument that maximizes the integral in 0≤α≤5 using FindArgMax:
Properties & Relations (8)
MellinConvolve computes the integral :
Convolution with DiracDelta:
Derivatives of DiracDelta:
The Mellin transform of a convolution is the product of the individual Mellin transforms:
Derivative of MellinConvolve with respect to y:
Relation between MellinConvolve, MellinTransform, and InverseMellinTransform:
Wolfram Research (2016), MellinConvolve, Wolfram Language function, https://reference.wolfram.com/language/ref/MellinConvolve.html.
Wolfram Language. 2016. "MellinConvolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MellinConvolve.html.
Wolfram Language. (2016). MellinConvolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MellinConvolve.html