二项式定理

The boon space Si say:Newton established astronomy because of discovering gravitational theory, because of carry on light of resolve but established the optics of science, established mathematics of science because of establishing binomial equation axioms and infinite theories, established the mechanics of science because of knowing the man's natural character of the mechanics.

恩格斯说：牛顿由于发现了万有引力定律而创立了天文学，由于进行光的分解而创立了科学的光学，由于创立了二项式定理和无限理论而创立了科学的数学，由于认识了力学的本性而创立了科学的力学。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

He initiated his pupils into the mysteries of the binomial theorem.

他给他的学生们讲授二项式定理的奥秘。

It included Karaji's binomial theorem and rules of the arithmetic polynomial operations and developed Karaji's theory of polynomial.

其中保存了凯拉吉的关於二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus.

1665年，他发现了广义二项式定理，并开始开发一种数学理论，后来成为微积分。

This book included Karaji's binomial theorem and rules of the arithmetic polynomial operations and it developed Karaji's theory of polynomial.

算术珍本》中保存了凯拉吉的关于二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

Evaluation of P is simplified if the square root terms are expanded by the binomial theorem.

如果按二项式定理展开来计算平方根，P的计算可以简化。

In mathematics, Newton established "the Newton binomial theorem", and nearly simultaneously established the calculus study with Leibniz.

在数学上，牛顿创立了"牛顿二项式定理"，并和莱布尼兹几乎同时创立了微积分学。

The binomial theorem expands powers of sums.

二项式定理扩大权力的高低。

Theorem g is called binomial theorem.

定理g称为二项式定理。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。