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The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series ∑k=0 ᪲α choose kxk, where α choose k=(α(α-1)(α-2)...(α-k+1))/(k!).
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- 2010, James Stewart, Calculus: Concepts and Contexts, Cengage Learning, page 612, Thus, by the Ratio Test, the binomial series converges if |x| < 1 and diverges if |x| > 1.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The binomial theorem.
Definition source: English Wiktionary via Wiktextract
Usage: broadly
Topics: mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
2 source translations are retained for this English entry.
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Finnish:
binomisarja
— Maclaurin series expansion of (1 + x)α
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German:
binomische Reihe
— Maclaurin series expansion of (1 + x)α
