LerchPhi
Usage
• LerchPhi[z, s, a] 给出Lerch超越函数  .
Notes
•  , 其中  的项被排除。 • LerchPhi[z, s, a, DoublyInfinite->True] 给出和式  . • LerchPhi 是Zeta和PolyLog的推广。 • 参见 Mathematica 全书 : 节 3.2.10.
Further Examples
In[1]:=
|
Out[1]=
|
Here we use the option .
In[2]:=
|
Out[2]=
|
LerchPhi satisfies an analog to the functional equation for the Zeta function.
In[3]:=
|
In[4]:=
|
Out[4]=
|
The definitions of the invariants and in terms of the half-periods and exclude a particular term. Similarly, Mathematica allows you to choose whether or not to include the singular term (if there is one) in the series for Zeta[s, a] and LerchPhi[z, s, a].
In[5]:=
|
Out[5]=
|
In[6]:=
|
Out[6]=
|
If there is no singular term the option has no effect.
In[7]:=
|
Out[7]=
|
In[8]:=
|
Out[8]=
|
This is a series expansion around .
In[9]:=
|
Out[9]=
|
|