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E41

[1FP]Write Taylor’s polynomial of \((1+x)^𝛼\) with \(𝛼 ∈ ℝ ⧵ ℕ\). (Infer a generalization of the binomial symbol \(\binom 𝛼 k \)). The associated Taylor series is called binomial series, it converges for \(|x|{\lt}1\).

Solution 1

[1FQ]

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  • Taylor's theorem
  • binomial, coefficient
  • binomial, series
  • series, binomial —
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