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单词 BinomialTheorem
释义

binomial theorem


The binomial theoremMathworldPlanetmath is a formulaMathworldPlanetmathPlanetmath for the expansion of (a+b)n, for n a positive integer and a and b any two real (or complex) numbers, into a sum of powers of a and b. More precisely,

(a+b)n=an+(n1)an-1b+(n2)an-2b2++bn.

For example, if n is 3 or 4, we have:

(a+b)3=a3+3a2b+3ab2+b3
(a+b)4=a4+4a3b+6a2b2+4ab3+b4.

This result actually holds more generally if a and b belong to a commutativePlanetmathPlanetmathPlanetmath rig (http://planetmath.org/Rig).

Titlebinomial theorem
Canonical nameBinomialTheorem
Date of creation2013-03-22 11:46:47
Last modified on2013-03-22 11:46:47
OwnerKimJ (5)
Last modified byKimJ (5)
Numerical id17
AuthorKimJ (5)
Entry typeTheorem
Classificationmsc 11B65
Classificationmsc 06F25
Classificationmsc 03E20
Related topicBinomialFormula
Related topicBinomialCoefficient
Related topicBernoulliDistribution2
Related topicUsingThePrimitiveElementOfBiquadraticField
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更新时间:2025/5/4 14:45:05