二项式系数

The binomial coefficient is the number of ways to choose k objects from a set of n objects, regardless of order.

二项式系数是很多的方法来选择k的物体从一组的N物体，不论顺序。

When counting the number of combinations, the terminology is generally "n choose k", and is known as the Binomial Coefficient

在计算组合的数量，一般术语"n取k"的，并作为著名的二项式系数

When q=1, this Gaussian coefficient identity changes the corresponding binomial coefficient identity.

当q=1时得到对应的普通二项式系数恒等式。

On two binomial coefficient s and their related combinatorial identities;2. Several identities on binomial coefficient s and trigonometric func tion values of special angles are obtained.

利用组合数学的一些技巧给出了切比雪夫多项式的通项表达式，并得到了一些二项式系数，特殊三角函数值的恒等

By transforming the interlace series type linear differential equation with coefficient containing binomial coefficients and arrangement number into the linear differential equation of successive integral,the theory and method for solving this kind of equation are determined.

通过把系数含有二项式系数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proofs on the subspace-lattice. Especially, one remarkable result is that a new q-analogue of the cube-sums identity is obtained with its combinatorial proof over the vector space.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从向量空间角度给出了一些恒等式的q-模拟及组合证明，其中突出的成果是给出了立方和恒等式的一个新的q-模拟及组合证明。

NMath Stats contains a data table class with functions for computing descriptive statistics, such as mean, variance, standard deviation, percentile, median, quartiles, geometric mean, harmonic mean, RMS, kurtosis, skewness, and many more; PDF, CDF, inverse CDF, and random variable moments for a variety of probability distributions, including normal, Poisson, chi-square, gamma, beta, Student's t, F, binomial, and negative binomial; Combinatorial functions, such as factorial, log factorial, binomial coefficient, and log binomial; Multiple linear regression; Basic hypothesis tests, such as z-test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals; One-way and two-way analysis of variance and analysis of variance with repeated measures; Multivariate statistical analyses, including principal component analysis and hierarchical cluster analysis.

nmath统计包含一个数据表的阶层与职能计算描述性统计，如平均，方差，标准差，百分位，中位数， 25 ％，几何平均数，调和的意思是，有效值，峭度，偏度，还有更多的； PDF格式，民防部队，逆民防部队，并随机变量矩的各种概率分布，包括正常，泊松，卡方检定，伽玛，测试版，学生的吨，男，二项式，并负二项分布；组合的功能，例如阶乘，日志阶乘，二项式系数，并登入二项式；多元线性回归；基本假设测试，如的Z测试， t检验， F检验，计算p值，临界值，和置信区间；之一，双向和双方法方差分析和方差分析与反复的措施；多元统计分析，包括主成分分析和聚类分析。

This method reveals the combinatorial connections between the binomial coefficients and the Gaussian coefficients.

这种证明方法深刻地揭示了高斯系数和二项式系数之间的组合联系。

The relations expressing the corresponding changes of the Factor A and Factor B in the binomial with the deviation factor and viscosity of natural gas are derived in the paper.

文章推导出二项式系数A、B随天然气偏差系数和粘度对应变化的关系式。

In this paper, we discuss some recurrence relations and congruence properties of Bell polynomial, and give a class of recurrence relations satisfied by GSN pairs. Furthermore, we givethe definition of extended GSN pairs Gand G, so we unify the binomial coefficients, Gaussian coefficients, and Stirling numbers. We provide urn ,models for G(n,k|w,0) andG(n,k|0,w).

在这篇论文中，我们讨论了Bell多项式中的递归关系和同余问题，给出了广义Stirling数对的一类递归关系式，提出了扩展的GSN对G和G的概念，统一了二项式系数、高斯系数和Stirling数，并利用模型对G和G进行了组合解释。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。