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)

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

• Prev by Date: Re: Problems with differentiating Piecewise functions
• Next by Date: Re: Tally
• Previous by thread: Limit[(x - Log[Cosh[x]]) SinIntegral[x], x -> Infinity]
• Next by thread: Re: Re: Limit[(x - Log[Cosh ]) SinIntegral , x -> Infinity]