You can't simply say that the expansion at infinity equals the expansion of at . That wouldn't make any sense.

But

so

Would that then be considered the expansion at infinity? And would it be valid for x >1?

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- January 12th 2011, 02:22 PMRandom Variabletaylor expansion of arctan(x) at infinity

You can't simply say that the expansion at infinity equals the expansion of at . That wouldn't make any sense.

But

so

Would that then be considered the expansion at infinity? And would it be valid for x >1? - January 12th 2011, 02:55 PMzzzoak

RHS is true when |x|<1. Then LHS is true when 1/x goes to infinity.

Making substitution

y=1/x where y goes to infinity we get

this is what you get. - January 12th 2011, 03:22 PMRandom Variable
But for what values is the series valid? It would appear that it's valid for x=1.

- January 12th 2011, 03:59 PMzzzoak
It is valid for

and it follows that

- January 12th 2011, 07:58 PMchisigma