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binomial theorem

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(mathematics) A formula giving the expansion of a binomial such as ( a + b ) raised to any positive integer power, i.e. ( a + b )^{n} . It's possible to expand the power into a sum of terms of the form ax^{b}y^{c} where the coefficient of each term is a positive integer. For example:

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algebraic expansion of powers of a binomial
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Maybe using the binomial theorem, that would take a while.
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The paper draws an analogy between the binomial theorem and the successive derivatives of the product of functions.
투명 플렉시블 하드코팅 필름 및 이의 제조 방법ParaCrawl Corpus ParaCrawl Corpus
In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus .
고무제 또는 경화섬유제 좌금 (座金)ParaCrawl Corpus ParaCrawl Corpus
He goes on to consider solid geometry giving results on prisms, cylinders, and spheres. In Book 9 Saunderson presents the binomial theorem and the theory of logarithms.
가소제 (可塑劑)ParaCrawl Corpus ParaCrawl Corpus
At the academy Gauss independently discovered Bode's law, the binomial theorem and the arithmetic- geometric mean, as well as the law of quadratic reciprocity and the prime number theorem.
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However, he was more interested in mathematics than he was in the law and at the age of 20 Buffon (he was now calling himself Georges-Louis Leclerc De Buffon) discovered the binomial theorem .
결정성 이산화티탄(TiO2) 분말의 제조방법, 음극 활물질의 제조 방법, 음극 활물질 및 리튬 이차 전지에 관한 것으로서, 상기 결정성 이산화티탄 분말의 제조 방법은 사염화티타늄(TiCl4)을 0°C 내지 10°C의 물에 첨가하여 티타닐클로라이드 (TiOCl2) 수용액을 제조하는 단계; 상기 티타닐클로라이드 수용액에 알코올, 요소 및 구형화제를 첨가하여 혼합물을 제조하는 단계; 및 상기 혼합물을 1.5 기압(atm) 내지 5 기압(atm)의 압력 및 80°C 내지 155°C의 온도에서 수열합성 반응을 실시하 는 단계를 포함한다.ParaCrawl Corpus ParaCrawl Corpus
As an example of Aepinus' less good work, the authors of relate that in 1763 Aepinus published in Latin in the Commentaries of the St Petersburg Academy a proof of the binomial theorem for real values of the exponent.
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Guinand worked on summation formulae and prime numbers , the Riemann zeta function , general Fourier type transformations, geometry and some papers on a variety of topics such as computing, air navigation, calculus of variations , the binomial theorem , determinants and special functions .
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Although Pascal was not the first to study the Pascal triangle , his work on the topic in Treatise on the Arithmetical Triangle was the most important on this topic and, through the work of Wallis , Pascal's work on the binomial coefficients was to lead Newton to his discovery of the general binomial theorem for fractional and negative powers.
레시틴 식이보충제ParaCrawl Corpus ParaCrawl Corpus
This excellent book records the main achievements which include the following: methods for giving accurate approximate solutions of cubic equations ; work with the binomial theorem ; Ulugh Beg's accurate tables of sines and tangents correct to eight decimal places; formulae of spherical trigonometry; and of particular importance, Ulugh Beg's Catalogue of the stars, the first comprehensive stellar catalogue since that of Ptolemy .
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He also worked on independent binomial trials and his most important contribution was his statement of the criticality theorem for simple branching processes which he gave in 1845.
상기 상관성 유효 평가에 의해 상기 위치 정보가 상기 측정 결과에 대해 높은 상관성을 가지는 것으로 결정되면, 상기 방법은 상기 위치 정보를 상기 기지국으로 전송하는 것을 더 포함한다.ParaCrawl Corpus ParaCrawl Corpus
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