       InverseSeries for x->Infinity

• To: mathgroup at smc.vnet.net
• Subject: [mg117540] InverseSeries for x->Infinity
• From: enrique rame <enrique.rameNOSPAM at grc.nasa.gov>
• Date: Tue, 22 Mar 2011 05:07:14 -0500 (EST)

```Hi,

I made up a simple example to test the InverseSeries function when the
variable goes to Infinity. I defined the function x^2, expanded it as x-
>Inf, then get the InverseSeries, then get the InverseSeries again.
Instead of returning to the original function, the system returns 1 over
the original function. As far as I can tell, the problem only happens
for x-> Inf, and when the original series has a fractional leading power.
This problem does not happen when the series is about x->0, or when the
series is about Infinity but the leading power is integer. Am I doing
something wrong here?

Here's the Mathematica code that illustrates the problem I'm having:

In:= f[x_] = x^2

Out= x^2

In:= Series[f[x], {x, Infinity, 2}]

Out= x^2 + O[1/x]^3

In:= InverseSeries[Series[f[x], {x, Infinity, 2}], y]

Out= Sqrt[y] + O[1/y]^2

In:= InverseSeries[%, x]

1/x^2 + O[x]^3

Thanks,
-enrique

--
Enrique Rame
433-2842
enrique.rame at grc.nasa.gov

The opinions expressed here are only mine and do not represent positions
of NASA.

```

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