complex-analysis
Taylor series of complex functions
taught
Every function analytic on a disk equals its own Taylor series there -- a guarantee real analysis never gives, proved from the Cauchy integral formula.
Taught in
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Taylor's theorem for analytic functions
Complex Analysis
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Uniform convergence and term-by-term calculus
Complex Analysis
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Uniqueness of power series representations
Complex Analysis
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Multiplying and dividing power series
Complex Analysis
Requires
- complex-power-series-convergence required
- cauchy-integral-formula required
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taylor-and-maclaurin-series
helpful
The real-variable version of the same series, without the automatic convergence guarantee analyticity provides here.
Required by
- Analytic continuation required
- Laurent series required
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Local knowledge map
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