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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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.
But for what values is the series valid? It would appear that it's valid for x=1.
It is valid for and it follows that
Originally Posted by Random Variable 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? The series... (1) ... is a Laurent series and not a Taylor series!... it converges for and f(*) has a single essential singulatity in z=0... Kind regards
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