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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86947] Re: Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]
  • From: "Szabolcs HorvÃt" <szhorvat at gmail.com>
  • Date: Thu, 27 Mar 2008 08:16:21 -0500 (EST)
  • References: <20080326082007.401$ci@newsreader.com>

On Wed, Mar 26, 2008 at 1:20 PM, David W. Cantrell
<DWCantrell at sigmaxi.net> wrote:
>  I confirm the precise behavior you described. It's surprising that a
>  restart was required.

Actually a ClearSystemCache[] is enough, but since cached results can
affect the success of calculations, probably it would be better if
Mathematica did not cache the "result" that it *cannot* calculate
something.

>
>  In[4]:= ClearSystemCache[]
>
>  In[5]:= Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]
>
>  Out[5]= Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]
>
>  In[6]:= Limit[FullSimplify[(x - Log[Cosh[x]]) SinIntegral[x], x > 0],
>   x -> Infinity]
>
>  Out[6]= (1/2)*Pi*Log[2]
>
>  Note that using FullSimplify merely changes -Log[Cosh[x]] to +Log[Sech[x]],
>  but curiously, that seems to help.

Hmm, this does not work for me:

In[1]:= Limit[FullSimplify[(x - Log[Cosh[x]])*SinIntegral[x], x > 0],
                  x -> Infinity]

Out[1]= Limit[(x + Log[Sech[x]])*SinIntegral[x], x -> Infinity]

I get back the same expression even if I evaluate all 6 input cells in turn.

In[2]:= $Version
Out[2]= "6.0 for Microsoft Windows (32-bit) (February 7, 2008)"

Szabolcs


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