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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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