asymptotics

• To: mathgroup at smc.vnet.net
• Subject: [mg76613] asymptotics
• From: dimitris <dimmechan at yahoo.com>
• Date: Thu, 24 May 2007 06:23:26 -0400 (EDT)

```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^2*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

```

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