形式幂级数技巧的应用——Ⅰ.李善兰恒等式的初等证明

本文应用形式幂级数的计算技巧,得到二元序列?之母函数的封闭形 式,进而给出李善兰恒等式的一个初等证明。     

优序理论与平面分析(V)

Let E_λ~(n)(n;q) denote the GF for ordinary plane partitions of shape λ with part restrictions and n (i.e., the parts in ith row are not less than n_i and the largest part in partitions does not exceed n). By establishing the correspondence between reverse plane partitions and ordinary plane partitions,we have derived the following determinant expression.     

优序理论与平面分析(Ⅳ)

Let RG_λ(q) denote the GF for row and column-strict reverse plane par titions of shape λ with part restriction (i.e., the parts in ith row do not exceed n_i). Using the correspondence similar to that in section Ⅲ with the same title, we have the following determinant expression.     

Some Bivariate Inverse Relations With Applications to Interpolation Formulae

This paper investigates the bivariate analogs of Gould-Hsu's inversions and obtains an inverse relation including five sets of free parameters which can be seen as a partial solution for Hsu's open problem. Some instances and applications to interpolation theory are remarked.     

优序理论与平面分析(Ⅲ)

Let RF_λ=(q) denote the GF for column-strict reverse plane partitions of shape λ with part restriction (i.e., the parts in ith row do not exceed n_i). By introducing the correspondence of reverse plane partitions without and with column-strict restriction, we have the following determinant expression.     

基本超几何级数--恒等式快速入门

基本超几何级数之重要性已被学术界广泛认识.关于这一迅速发展的学科分支,多数读者更加需要介绍性文章.作者将沿着这一方向作一尝试.     

关于多项式系数的Jensen定理及其Abel模拟

将Gould的形式幂级数的计算技巧运用到多元函数,作者证明了关于多项式系数卷积计算的Jensen定理及其Abel形式。所得结果可以视为Mohanty和作者以前工作的自然延伸和拓广。