Re: asymptotics
- To: mathgroup at smc.vnet.net
- Subject: [mg76798] Re: asymptotics
- From: m.r at inbox.ru
- Date: Sun, 27 May 2007 05:06:05 -0400 (EDT)
- References: <f33qsc$mc6$1@smc.vnet.net>
On May 24, 5:54 am, dimitris <dimmec... at yahoo.com> wrote:
> Sorry fellas if I ask something trivial
> but currently I can't find anything!
>
> In another CAS I took
>
> f:=asympt(exp(-y*sqrt(1+m^2*u^2)/m),u,5);
>
> / 2 1/2 2 2 1/2 2 2
> | y (m ) y y (m ) (-6 m + y )
> f := |1 - --------- + ------- - ----------------------
> | 3 4 2 7 3
> \ 2 m u 8 m u 48 m u
>
> 2 2 2 \ 2 1/2
> y (-24 m + y ) 1 | / y (m ) u
> + ---------------- + O(----)| / exp(-----------)
> 8 4 5 | / m
> 384 m u u /
>
> ff:=simplify(convert(f,polynom)) assuming m>0;
> ff := 1/384*exp(-
> y*u)*(384*m^8*u^4-192*y*m^6*u^3+48*y^2*m^4*u^2+48*y*m^4*u-8*y^3*m^2*u-24*=
y^=AD2*m^2+y^4)/
> m^8/u^4
>
> In Mathematica I can't get the expansion in infinity
>
> In[113]:= Series[Exp[(-y)*(Sqrt[1 + m^2*u^2]/m)], {u, Infinity, 10}]
> Out[113]= E^(-((Sqrt[1 + m^2*u^2]*y)/m))
>
> What do I miss here?
>
> Thanks
> Dimitris
You can divide out the part that contributes the essential
singularity:
In[1]:= E^(-y u Sqrt[m^2]/m) Series[
E^(-y Sqrt[1 + m^2 u^2]/m + y u Sqrt[m^2]/m),
{u, Infinity, 4}] // InputForm
Out[1]//InputForm= SeriesData[u, Infinity, {1, -(Sqrt[m^2]*y)/(2*m^3),
y^2/(8*m^4),
(6*(m^2)^(3/2)*y - Sqrt[m^2]*y^3)/(48*m^7),
(-24*m^2*y^2 + y^4)/(384*m^8)}, 0, 5, 1]/E^((Sqrt[m^2]*u*y)/m)
Maxim Rytin
m=2Er at inbox.ru