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Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86932] Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Wed, 26 Mar 2008 04:56:04 -0500 (EST)
  • Organization: University of Bergen

I expected that Limit would try to compute the limit of terms in a 
product separately.  Perhaps this is not feasible because of the large 
number of possible combinations?

In the following example it can give result for the terms separately, 
but not for the product:

In[1]:= Limit[(x - Log[Cosh[x]])*SinIntegral[x], x -> Infinity]
Out[1]= Limit[(x - Log[Cosh[x]])*SinIntegral[x], x -> Infinity]

In[2]:= Limit[x - Log[Cosh[x]], x -> Infinity]
Out[2]= Log[2]

In[3]:= Limit[SinIntegral[x], x -> Infinity]
Out[3]= Pi/2

In[4]:= Limit[(x - Log[Cosh[x]])*SinIntegral[x], x -> Infinity]
Out[4]= Limit[(x - Log[Cosh[x]])*SinIntegral[x], x -> Infinity]

(Note that In[4] still didn't give a result.)

However, if the evaluations are done in a different order (after a 
kernel restart), it is able to compute the result:

In[1]:= Limit[x - Log[Cosh[x]], x -> Infinity]
Out[1]= Log[2]

In[2]:= Limit[SinIntegral[x], x -> Infinity]
Out[2]= Pi/2

In[3]:= Limit[(x - Log[Cosh[x]])*SinIntegral[x], x -> Infinity]
Out[3]= (1/2)*Pi*Log[2]


Are there any options (perhaps SystemOptions) that would allow Limit to 
give an answer directly for the product of the terms?


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