Find an Inverse Mellin Transform
Compute an inverse Mellin transform using InverseMellinTransform.
In[1]:=
![Click for copyable input](assets.en/find-an-inverse-mellin-transform/In_6.png)
InverseMellinTransform[Gamma[s], s, x]
Out[1]=
![](assets.en/find-an-inverse-mellin-transform/O_6.png)
Obtain the strip of holomorphy assumed by InverseMellinTransform.
In[2]:=
![Click for copyable input](assets.en/find-an-inverse-mellin-transform/In_7.png)
InverseMellinTransform[Gamma[s], s, x, GenerateConditions -> True]
Out[2]=
![](assets.en/find-an-inverse-mellin-transform/O_7.png)
Compute an inverse Mellin transform leading to BesselJ.
In[3]:=
![Click for copyable input](assets.en/find-an-inverse-mellin-transform/In_8.png)
InverseMellinTransform[(2^(-1 + s) a^-s Gamma[1/2 + s/2])/
Gamma[3/2 - s/2], s, x]
Out[3]=
![](assets.en/find-an-inverse-mellin-transform/O_8.png)
Plot the result for different values of .
In[4]:=
![Click for copyable input](assets.en/find-an-inverse-mellin-transform/In_9.png)
InverseMellinTransform[(2^(-1 + s) a^-s Gamma[1/2 + s/2])/
Gamma[3/2 - s/2], s, x];
Plot[Table[% , {a, 1, 5}] // Evaluate, {x, 0, 7}]
Out[4]=
![](assets.en/find-an-inverse-mellin-transform/O_9.png)
Create a table of basic inverse Mellin transforms.
show complete Wolfram Language input
Out[5]//TraditionalForm=
![](assets.en/find-an-inverse-mellin-transform/O_10.png)