【摘要】：本文第一部分首先給出了q-Delannoy數(shù)Dq*(m,n)的Lucas型同余式的代數(shù)證明,并給出了Dq(m,n)滿足的遞歸式的代數(shù)證明.第二部分給出了一個關(guān)于兩個q-Delannoy數(shù)乘積的求和公式,并使用它證明了關(guān)于q-Delannoy數(shù)求和的一些同余式.這一結(jié)論證明了郭軍偉教授近期的三個猜想.我們進一步推廣了這一求和公式,證明了某一 6Φ5型級數(shù)可以分解成兩個3Φ2型級數(shù)的乘積.這個推廣的公式可以看做Slater書中一求和公式的終止形式的q-模擬.
[Abstract]:In the first part of this paper, the algebraic proof of the Lucas type congruence of q-Delannoy number Dq* (MGN) is given, and the algebraic proof of the recursion formula satisfied by Dq (MGN) is given. In the second part, we give a summation formula about the product of two q-Delannoy numbers, and prove some congruences about the sum of q-Delannoy numbers. This conclusion confirms Professor Guo Junwei's recent three conjectures. We further generalize this summation formula and prove that a series of type 6 桅 5 can be decomposed into the product of two series of type 3 桅 2. This generalized formula can be regarded as a quasi-simulation of the termination form of a sum formula in Slater's book.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O156

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1 郭紅芳;關(guān)于q-Delannoy數(shù)的一些性質(zhì)[D];華東師范大學(xué);2017年

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本文編號：2294387