求梅林逆变换
用 InverseMellinTransform 计算梅林逆变换.
In[1]:=
![Click for copyable input](assets.zh/find-an-inverse-mellin-transform/In_6.png)
InverseMellinTransform[Gamma[s], s, x]
Out[1]=
![](assets.zh/find-an-inverse-mellin-transform/O_6.png)
获取由 InverseMellinTransform 认定的全纯带.
In[2]:=
![Click for copyable input](assets.zh/find-an-inverse-mellin-transform/In_7.png)
InverseMellinTransform[Gamma[s], s, x, GenerateConditions -> True]
Out[2]=
![](assets.zh/find-an-inverse-mellin-transform/O_7.png)
计算一个给出 BesselJ 的梅林逆变换.
In[3]:=
![Click for copyable input](assets.zh/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.zh/find-an-inverse-mellin-transform/O_8.png)
对 a 取不同值的结果绘图.
In[4]:=
![Click for copyable input](assets.zh/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.zh/find-an-inverse-mellin-transform/O_9.png)
创建一个基本梅林逆变换的表格.
显示完整的 Wolfram 语言输入
Out[5]//TraditionalForm=
![](assets.zh/find-an-inverse-mellin-transform/O_10.png)