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GenericIntegralTransform (1.1.0) current version: 3.1.4 »

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Compute a variety of integral transforms on input expressions

Contributed by: Paco Jain & Oleg Marichev

ResourceFunction["GenericIntegralTransform"][f,z,t,"type"]

gives the integral transform 𝒯_type[f](t) corresponding to the input function f(z), in terms of the new variable t.

Details and Options

ResourceFunction["GenericIntegralTransform"] supports the following options:

GenerateConditions

True

whether to provide conditions under which the given result is valid

"FoxHForm"

False

whether to provide results (where possible) in terms of the FoxH function

Currently supported values for "transform" include: "Mellin".

Examples

Basic Examples (2)

Compute the Mellin transform of a Bessel function:

In[1]:=

$ResourceFunction["GenericIntegralTransform"][ BesselJ[\[Nu], z], z, t, "Mellin"]$

Out[1]=

Compute the Mellin transform of an exponential function. Generically, the result returned is a ConditionalExpression:

In[2]:=

Out[2]=

The conditions under which this result holds can be expanded by clicking the "+", followed by "Uniconize":

In[3]:=

$ConditionalExpression[ a^-s Gamma[ s], (Abs[Arg[a]] < \[Pi]/2 && 0 < Re[s] < \[Infinity]) || (Abs[Arg[a]] == \[Pi]/2 && 0 < Re[s] < \[Infinity] && -(1/2) + Re[s] < 1/2)]$

Options (2)

Using the option setting GenerateConditions→False to suppress convergence conditions from transform results:

In[4]:=

$ResourceFunction["GenericIntegralTransform"][ BesselJ[\[Nu], z], z, t, "Mellin", GenerateConditions -> False]$

Out[4]=

Contrast with the default setting GenerateConditions→True:

In[5]:=

$ResourceFunction["GenericIntegralTransform"][ BesselJ[\[Nu], z], z, t, "Mellin"]$

Out[5]=

Version History

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License Information

This work is licensed under a Creative Commons Attribution 4.0 International License