binomial theorem


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binomial theorem

n. Mathematics
The theorem that specifies the expansion of any power (a + b)m of a binomial (a + b) as a certain sum of products aibj, such as (a + b)2 = a2 + 2ab + b2.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

binomial theorem

n
(Mathematics) a mathematical theorem that gives the expansion of any binomial raised to a positive integral power, n. It contains n + 1 terms: (x + a)n = xn + nxn1a + [n(n–1)/2] xn2a2 +…+ (nk) xnkak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

bino′mial the′orem


n.
the theorem giving the expansion of a binomial raised to any power.
[1865–70]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.binomial theorem - a theorem giving the expansion of a binomial raised to a given power
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
probability theory, theory of probability - the branch of applied mathematics that deals with probabilities
theorem - a proposition deducible from basic postulates
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References in classic literature ?
At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue.
For t [member of] R andp, k [member of] [Z.sup.+], by the binomial theorem, the following identity holds:
Using the binomial theorem, we have from relations (3)
From the Binomial theorem, we get [([alpha] - [beta]).sup.p] [equivalent to] [[alpha].sup.p] - [[beta].sup.p] (modp).
In order to verify its superiority over other methods, its results have been compared with those of Newton binomial theorem and Dolph- Chebyshev method.
Among them are a simple numerical approach to the Riemann hypothesis, aunifying construction for measure-valued continuous and discrete branching processes, examples of quantitative universal approximation, harmonic mappings with quadilateral image, meromorphic approximation on noncompact Riemann surfaces, a family of outer functions, the universality of series in Banach space, recent progress on fine differentiability and fine harmonicity, reversibility questions in groups arising from analysis, and the generalized binomial theorem. There is no index.
By using the change of variable t = y/[square root of (p + [[alpha].sup.2][y.sup.2])], the binomial theorem, and term-by-term integration, the original integral can be expressed as
To test the Hardy-Weinburg demonstration that the genotype frequencies remain stable from one generation to the other, under certain conditions the general binomial theorem was used.
Add to that his Opticks (1704), his discovery of infinitesimal calculus and the binomial theorem, his formulation of the three fundamental laws of motion, his analysis of white light, and one has yet only a partial image of his genius.
Einstein considered the velocity in classical region thus applying binomial theorem,
of Texas-Dallas) has updated his 2001 textbook for advanced undergraduate and beginning graduate students who know calculus up to partial differentials, ordinary vectors to the point of differentiating them, and the binomial theorem. The second edition updates the material, particularly in three chapters on cosmology, and adds some new exercises.
i) Use the binomial theorem to write an expression for [t.sub.k], 0 [less than or equal to] k [less than or equal to] 25.