关于q-Delannoy数的一些性质
发布时间:2018-10-25 17:52
【摘要】:本文第一部分首先给出了q-Delannoy数Dq*(m,n)的Lucas型同余式的代数证明,并给出了Dq(m,n)满足的递归式的代数证明.第二部分给出了一个关于两个q-Delannoy数乘积的求和公式,并使用它证明了关于q-Delannoy数求和的一些同余式.这一结论证明了郭军伟教授近期的三个猜想.我们进一步推广了这一求和公式,证明了某一 6Φ5型级数可以分解成两个3Φ2型级数的乘积.这个推广的公式可以看做Slater书中一求和公式的终止形式的q-模拟.
[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.
【学位授予单位】:华东师范大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O156
本文编号:2294387
[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.
【学位授予单位】:华东师范大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O156
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1 郭红芳;关于q-Delannoy数的一些性质[D];华东师范大学;2017年
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