若干q-差分方程的形式解及其应用  

Some Formal Solutions of q-difference Equation and their Applications

作　　者：刘富裕 许敏[1] 曹健[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2017年第2期187-194,共8页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：随着非线性数学和量子数学的快速发展,组合数学中复杂的积分运算与有限的求和公式是制约研究进展的重要因素.本文构造以q-指数算子作为形式解的q-差分方程,并利用q-差分方程形式解方法推广Sears公式、Al-Salam-Carlitz多项式生成函数、Andrews-Askey积分、q-Chu-Vandermonde公式等.With the rapid development of nonlinear mathematics and quantum mathematics, in the combinatorial mathematics, the complexity of integral operation and the finiteness of summation formula are the important factors which restrict the progress of researches. This paper constructs the q difference equation with q exponential operator as the formal solution, and uses the formal solution way of q difference equation to generalize Sears formula, Al-Salam-Carlitz polynomial generating functions, Andrews-Askey integral, q-Chu Vandermonde formula, etc.

关 键 词：q-指数算子 q-差分方程 Andrews-Askey积分 q-Chu-Vandermonde公式 Sears公式 

分 类 号：O177.91[理学—数学]