gives the Mellin transform of expr.
gives the multidimensional Mellin transform of expr.
Details and Options
- The Mellin transform of a function is defined to be .
- The multidimensional Mellin transform of a function is given by .
- The Mellin transform of exists only for complex values of such that . In some cases, this strip of definition may extend to a half-plane.
- The following options can be given:
Assumptions $Assumptions assumptions on parameters GenerateConditions False whether to generate results that involve conditions on parameters Method Automatic what method to use
- In TraditionalForm, MellinTransform is output using .
Examplesopen allclose all
Basic Examples (2)
Basic Uses (3)
Elementary Functions (3)
Mellin transforms of polynomials are given in terms of DiracDelta:
Special Functions (3)
Piecewise Functions (3)
Attempting to evaluate this example by a conversion to MeijerG fails:
The default method uses a conversion to MeijerG for this example:
This example is evaluated using a numerical method based on NIntegrate:
Use MellinTransform to evaluate , which may be regarded as a Mellin convolution of the following functions:
Apply MellinTransform to each function:
Compute the integral directly using Integrate:
Obtain the same result using MellinConvolve:
Find the general solution of the Bessel equation using MellinTransform:
Apply MellinTransform to the equation:
Use RSolveValue to solve the recurrence equation:
Use InverseMellinTransform to find the required general solution:
Verify the result using DSolveValue:
Use MellinTransform to find the first two terms in the asymptotic expansion for a function that is defined by an infinite series:
Properties & Relations (11)
Use Asymptotic to compute an asymptotic approximation:
MellinTransform computes the integral :
Obtain the same result using Integrate:
MellinTransform is a linear operator:
Possible Issues (1)
Different expressions may have the same MellinTransform: