组合恒等式

用代数方法证明一个组合恒等式

Algebraic proof for the combinatorial identity

Cauchy组合恒等式的多种推广&兼谈幂级数一定理及其应用

The Generalization of Cauchy Combinatorial Identity ── on a Theorem and its Applications to Power Series

利用卷积公式，得到完全i-部图的计数公式（第二章），进一步研究了有关完全i-部图的组合恒等式，并通过N（（？）

By using of formulas of convolutions , the author obtains the counting formulas and combinatorial identities of complete i-partite graphs ( see Chapter 2 ) .

若干组合恒等式证明及广义的Bernoulli多项式、Euler多项式探析

Combinatorial Identities ' Proof and Research on the Generalized Bernoulli and Euler Polynomials

孪生组合恒等式（十）&推广Fibonacci数与推广Lucas数类型

Combinatorial Twin Identities (ⅹ): Generalized Fibonacci 's Number and Generalized Lucas 's Number Type

本文给出了第二类Stirling数的又一种一般表达式并从表达式（1）推出了一种新的组合恒等式其中P≥1。

Another general expression of stirling number of the second class is given and a new sort of combinatorial identities ( p ≥ 1 ) is obtained .

涉及广义Fibonacci数的组合恒等式

Combinatorial Identity Involving Generalized Fibonacci Numbers

利用这一表示，导出了若干q变形的组合恒等式，并用来证明了变形的双模Fock空间一种完备性关系。

From these developments , several useful q-deformed combinatorial identities are derived anti a new completeness relation in the q-deformed two-mode Fock space proved .

Vandermonde类型行列式与组合恒等式

Vandermonde typed determinant and combinatorial identity

Riemann-Zeta函数的超几何级数方法和组合恒等式

Hypergeometric Series Method for Riemann-Zeta Function and Combinatorial Identities

利用LagrangeBürmann反演公式得到了Vandermonde卷积公式，由此得到Abel恒等式的特殊情形和一些很有意义的组合恒等式。

In this paper , a Vandermonde-type convolution formula by using the Lagrange-B ü rmann inversion formula is presented . Furthermore , in virtue of this formula , the classical Abel identity as specific case and some significative combinatorial identities are obtained .

提出相伴数的定义，采用数学机械化的方法给出了相伴数的发生函数（第六章），给出了相伴数与Pell数，Fibonacci数和两类Chebyshev多项式之间的组合恒等式。

The author proposes a concept of associated numbers ( see Chapter 6 ), gives the generating functions by mechanized method , and discusses combinatorial formulas on associated numbers , finally , obtained a number of combinatorial identities related to Pell numbers , Fibonacci numbers and Chebyshev polynomials .

第二章介绍Wang-Ball曲线的定义及性质，以及Wang-Ball曲线的递归求值算法，利用Wang-Ball基函数的对偶泛函，作者在这里给出Wang-Ball曲线的显式细分算法，并由此导出几个计算组合恒等式。

Chapter two is focused on the Wang-Ball curves , including definition , properties and recursive algorithms . Using the dual functional of the Wang-Ball basis , the author derives the subdivision algorithms for the Wang-Ball curves for the first time and then obtains some identical equations of calculation combination .

古典概型在排列组合恒等式证明中的应用

Application of Classic Probability Model in Proving Permutation and Combination Identical Relation

二类切比雪夫多项式积和的几个组合恒等式

Some identical relations about the sum of Chebyshev polynomials product

用概率论的思想证明组合恒等式

Proving Equations of Combination by the Theory of Probability

刚玉宝石矿物新型组合恒等式

PRECIOUS STONES OF THE CORUNDUM MINERAL GROUP Combinatorial Identities of the New Type

J.Matrix定理的另一个推广及其在组合恒等式上的应用

Another generalization of I. J. matrix theorems and its application in combinatorial identities

用求导法则证明一类组合恒等式

The Proof of a Class of Combined Identity

两类组合恒等式的过渡方法

Transition method for two classes of combinatorial identities

两个组合恒等式的统一推广

The unified generalization of two combinatorial identities

以二项式作为生成函数，给出了几个组合恒等式证明。

In this paper , some combinatorial identities are proved based on binomial generating function .

反演技巧在组合恒等式中的应用

Applications of Inversion Techniques in Combinatorial Identities

孪生组合恒等式（二）

Combinatorial Twin Identity of the Type (ⅱ)

孪生组合恒等式（六）&三角类型

Combinatorial Twin Identity ⅵ: Trigonometric Type

关于几个组合恒等式的证明

The Proof of Some Combination Identities

有关二项式系数的2个组合恒等式

Two Combinatorial Identities Concerning Binomial Coefficients

本文运用形式幂级数的技巧，证明了一个重要的组合恒等式。

In this paper , an important combinatorial identity is obtained by means of the formal power series .

三个新的组合恒等式

Three New Combinatorial Identities

关于卷积型组合恒等式的格路方法（Ⅱ）&赋权格路的枚举函数方法

On the Lattice Path Method in Convolution Type Combinatorial ldentities (ⅱ) & The Weighted Counting Function Method on Lattice Paths