# binomial theorem

## Definitions

• WordNet 3.6
• n binomial theorem a theorem giving the expansion of a binomial raised to a given power
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Webster's Revised Unabridged Dictionary
• Binomial theorem (Math) See under Binomial.
• Binomial theorem (Alg) the theorem which expresses the law of formation of any power of a binomial.
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Chambers's Twentieth Century Dictionary
• Binomial theorem a series of analytical formulæ by which any power of a binomial can be expressed and developed
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## Etymology

Chambers's Twentieth Century Dictionary
L. bi-, bis, twice, and nomen, a name, a term.

## Usage

### In literature:

At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue.
"Memoirs of Sherlock Holmes" by Sir Arthur Conan Doyle
A chapter catches my attention in the middle of the volume; it is headed, Newton's Binomial Theorem.
"The Life of the Fly" by J. Henri Fabre
The activity of mind awakened by music over waters is very different from that awakened by the binomial theorem.
"The Theory of the Theatre" by Clayton Hamilton
Later still, he made what seemed to be approaches toward Newton's binomial theorem.
"Classic French Course in English" by William Cleaver Wilkinson
Why, as far back as when I was studying algebra, I nobly refused to learn the binomial theorem.
"At the Sign of the Jack O'Lantern" by Myrtle Reed
Natural Science is not the invention of man, more than is the law of gravitation, the law of equilibrium, or the binomial theorem.
"The New Avatar and The Destiny of the Soul" by Jirah D. Buck
Expand each term by the binomial theorem, and let us fix our attention on the coefficient of y^(n - 1).
"Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7" by Various
The answer to this question is the binomial theorem.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
Later still he made what seemed to be approaches toward Newton's binomial theorem.
"French Classics" by William Cleaver Wilkinson
You might as well try to rush the Proof of the Binomial Theorem.
"The Eulogy of Richard Jefferies" by Walter Besant
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### In poetry:

For, as their nurses dandle them
They crow binomial theorem,
With views (it seems absurd to us)
On differential calculus.
"My Dream" by William Schwenck Gilbert

### In science:

To prove Theorem 3 we need only establish the cutoff points for the expansion of the binomials in (3.1).
A Generalized Closed Form For Triangular Matrix Powers
In Theorem 3.3, we show that a given set of binomials generates I (X ).
Vanishing ideals over complete multipartite graphs
In Section 3, we describe 3 families of binomials and prove that they form a generating set for I (X ) — Theorem 3.3.
Vanishing ideals over complete multipartite graphs
By [14, Theorem 4.5] there exists a set of generators of I (X ) consisting of the generators of type I, plus a ﬁnite set of homogeneous binomials ta − tb with supp(a) ∩ supp(b) =
Vanishing ideals over complete multipartite graphs
The next theorem gives a class of functions for which the distribution of the total number of customers in the system in steady state is negative binomial.
Queues with random back-offs
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