Re: solve
- To: mathgroup at smc.vnet.net
- Subject: [mg38181] Re: [mg38144] solve
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Wed, 4 Dec 2002 03:26:08 -0500 (EST)
- In-reply-to: <200212030935.EAA14883@smc.vnet.net>
- References: <200212030935.EAA14883@smc.vnet.net>
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Thomas Garschall" <www at chello.at> wrote on Tuesday, December 03, 2002, 5:35:51 AM :
TG> i have a problem with the solving of the following with mathematica:
TG> given: vmin, vmax, z
TG> W=Integr[v^2*e^(-v^2/z^2)dv, vmin, vmax]
TG> because the resolution is something with "erf[]", but how can I solve
TG> erf[]???
Do you mean "the solution involves Erf[]"? If so, so what?
By definition, Erf[z] is 2/Sqrt[Pi] Integrate[Exp[-t^2], {t, 0, z}]
so to eschew Erf[z] you can make the global replacement but, as for
me, it makes not too much sense. In fact, you cannot express your
integral in terms of elementary functions, and must resort to special
functions.
In[1] := Integrate[v^2*E^(-v^2/z^2), {v, a, b}]
Out[1] = -(z^2*(-2*a + E^(a^2/z^2)*Sqrt[Pi]*z*Erf[a/z]))/(4*E^(a^2/z^2)) +
(z^2*(-2*b + E^(b^2/z^2)*Sqrt[Pi]*z*Erf[b/z]))/(4*E^(b^2/z^2))
In[2] := % // FullSimplify
Out[2] = (z^2*((2*a)/E^(a^2/z^2) - (2*b)/E^(b^2/z^2) + Sqrt[Pi]*z*(-Erf[a/z] +
Erf[b/z])))/4
and it is not possible to do without Erf's.
Best wishes,
Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group
http://www.CAS-testing.org/ GEMM Project (95% ready)
Email: vvb at mail.strace.net
Voice: (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
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Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine
- References:
- solve
- From: "Thomas Garschall" <www@chello.at>
- solve