二项式的

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。

In Chapter 2, by means of the integral theory, a number of reciprocal series involving binomial coefficients have been established and some results related to binomial coefficients have been extended.

本章利用定积分的方法和常见的发生函数，结合一些运算技巧，建立了一些与二项式系数的倒数有关的恒等式。

The frequency of observations in both the region just above and that just below zero departs significantly from the expected frequency under the normal distribution at the 1% significance level using the binomial test.

频率的意见都略高于该地区，并略低于零背离预期的有很大的频率下正常分配的1 ％显着性水平使用二项式测试。

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。

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。

Gauss is a farmer's son, childhood, his math on the show extraordinary talent. Three-year-old father to correct an error in calculation; They found 10-year-old independent series of arithmetic summation of the formula; 11-year-old found the binomial theorem.

高斯是一个农民的儿子，幼年时，他在数学方面就显示出了非凡的才华。3岁能纠正父亲计算中的错误；10岁便独立发现了算术级数的求和公式；11岁发现了二项式定理。

Having discussed Wallis'interpolation in great detail, the paper shows that Wallis mainly relied on incomplete induction and analogical inference to obtain his results, an approach which was key to the creation of many important algorithms during the considered period. A comparison between Wallis'method and previous interpolations is then made and the influence of Wallis' thinking style embodied in his interpolation on Newton's invention of binomial theorem is clearly revealed.

通过考察沃里斯的插值过程，指出沃里斯插值法完全是借助于不完全归纳和类比推理得到的，并与过去的插值法做了比较，最后分析了沃里斯插值法对牛顿发明二项式定理的影响。

Chart -- A discrete control chart. Based on the binomial distribution, fraction defective, p, is the ratio of the number of defective items, x, in a sample of size n.

图 --一种基于二项式分布的计数值控制图，它反映的是有缺陷产品的比率。P就是样本容量为n时，有缺陷产品x的比率。

And thus we ve worked out a new recursion formula of power sum problem ,using it ,we can get the calculationg formula of all the power sum problem .

本文利用二项式定理得到K =8，9，10 ，11时幂和∑ni=1ik 的计算公式，较文[1 ] 中结果表达式简单，并推出了关于幂和问题的一个新的递推公式，利用它可导出所有幂和问题的计算公式。

It is shown by the calculation result of the well Heba1 deliverability that the open flow potential by pseudo pressure binominal exponential deliverability taking stress sensitivity into consideration is more coincidence with the actual, which is of reference in developing such gas reservoir with high pressure.

河坝1井的产能计算结果表明，考虑应力敏感的拟压力二项式产能方程所计算的无阻流量更加符合实际，对于开发类似高压气藏具有一定的参考意义。

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％。