Re: Why two results of same eq. are different?

• To: mathgroup at smc.vnet.net
• Subject: [mg44808] Re: Why two results of same eq. are different?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Thu, 27 Nov 2003 11:38:43 -0500 (EST)
• Organization: NewsReader.Com Subscriber
• References: <200311200816.DAA01508@smc.vnet.net> <bpkpd7\$ce1\$1@smc.vnet.net> <bpuqr4\$o6s\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Tanel Telliskivi" <maria.08.6689847 at telia.com> wrote:
> Hello,
> "4.1 for Microsoft Windows (December 11, 2000)"
>
> In[2]:=
> f[a_]=Integrate[Log[2,1+10*x]*Exp[-x]*x,{x,0,a},Assumptions\[Rule]a>0]
>
> Out[2]=
> -((1/(20*Log[2]))*((20 - 20*E^a + 18*E^(1/10 + a)*
>       ExpIntegralEi[-(1/10)] + 18*E^(1/10 + a)*Gamma[0, 1/10 + a] +
>      9*E^(1/10 + a)*Log[1/(-1 - 10*a)] - 9*E^(1/10 + a)*
>       Log[-1 - 10*a] + 20*Log[1 + 10*a] + 20*a*Log[1 + 10*a] +
>      18*E^(1/10 + a)*Log[1 + 10*a])/E^a))

I'll assume that the intervening steps were to take the limit of that as
a -> Infinity, and then to evaluate numerically.

> Out[4]=
> 4.05855803419172 + 0.*I

That's fine if you're still using version 4. But, as I already pointed out,
in version 5, we have a bug. (It's a _retrograde_ bug.)

In[1]:=
Integrate[Log[2, 1 + 10*x]*Exp[-x]*x, {x, 0, a}, Assumptions -> a > 0]

Out[1]=
(10 + E^a*(-10 + 11*E^(1/10)*ExpIntegralEi[-(1/10)] +
11*E^(1/10)*Gamma[0, 1/10 + a]) - 10*(1 + a)*Log[1 + 10*a])/(E^a*(10*Log[2]))

In[2]:=
Limit[%, a -> Infinity]

Out[2]=
(-10 - 11*E^(1/10)*Gamma[0, 1/10])/(10*Log[2])

In[3]:=
N[%]

Out[3]=
-4.63986133014525

which is clearly wrong.

David Cantrell

```

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