Mathematica 9 is now available

LerchPhi

Usage

LerchPhi[z, s, a] 给出Lerch超越函数 .


Notes

• 数学函数(参见 节 A.3.10).
 , 其中  的项被排除。
LerchPhi[z, s, a, DoublyInfinite->True] 给出和式 .
LerchPhiZetaPolyLog的推广。
• 参见 Mathematica 全书: 3.2.10.
• 相关包: NumberTheory`Ramanujan`.
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]=



Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.