Are there instances when a Taylor series and a Laurent series of the same function about the same point ever equal?

Tiffany Page

Tiffany Page

Answered question

2022-11-12

Are there instances when a Taylor series and a Laurent series of the same function about the same point ever equal?

Answer & Explanation

Deanna Sweeney

Deanna Sweeney

Beginner2022-11-13Added 14 answers

Laurent series is unique. If a function has a Taylor series and a Laurent series about a point then the two coincide. Which means the function is analytic at that point.
Uriah Molina

Uriah Molina

Beginner2022-11-14Added 7 answers

The essential difference between Taylor and Laurent series at a point is their ranges of expansions. When you expand a function by Laurent series at a point, that point is not included in the range of expansion, while for Taylor series, it is included. In other words, the range for Laurent series is ring, for Taylor is circle.

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