Re: Integrate[e/(1+Exp[e]),{e,ei,Infinity}]
- To: mathgroup at yoda.physics.unc.edu
- Subject: Re: Integrate[e/(1+Exp[e]),{e,ei,Infinity}]
- From: withoff
- Date: Fri, 11 Dec 92 15:08:33 CST
> Integrate[e/(1+Exp[e]),{e,ei,Infinity}]
> this fermintegral of order 1 results in RecursionLimit errors.
> The indefinite integral can be found without any problems.
> Any ideas how to change the situation??
>
> Michael Trott
>
> trott at physik.tu-ilmenau.de
If the indefinite integral works, it can probably be used to compute
the definite integral. The built-in Limit function can't handle the
limit at Infinity, but the package Calculus`Limit` can.
In[1]:= f = Integrate[e/(1+Exp[e]),e]
2
e e e
Out[1]= -- - e Log[1 + E ] - PolyLog[2, -E ]
2
In[2]:= << Calculus`Limit`
In[3]:= Limit[f, e -> Infinity]
2
Pi
Out[3]= ---
6
In[4]:= Limit[f, e -> ei]
2
ei ei ei
Out[4]= --- - ei Log[1 + E ] - PolyLog[2, -E ]
2
In[5]:= %% - %
2 2
-ei Pi ei ei
Out[5]= ---- + --- + ei Log[1 + E ] + PolyLog[2, -E ]
2 6
Dave Withoff
withoff at wri.com