This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 LerchPhi LerchPhi[ z , s , a ] gives the Lerch transcendent . Mathematical function (see Section A.3.10). , where any term with is excluded. LerchPhi[ z , s , a , DoublyInfinite->True] gives the sum . LerchPhi is a generalization of Zeta and PolyLog. See the Mathematica book: Section 3.2.10. Related package: 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 usual notation for a sum that excludes a particular term is , as, for example, in the definitions of the invariants and in terms of the half-periods \[Omega] and . Mathematica simply 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]=