共查询到17条相似文献,搜索用时 46 毫秒
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本文利用初等方法简捷地推了Paule的结果,从而得到了一系列多重Rogers-Ramanujan恒等式。 相似文献
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本文利用一个已知的变换公式及其它基本超几何函数的求和公式,给出了一类q级数恒等式的新的更简单的证明,并建立了该类恒等式的一般形式. 相似文献
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本文利用初等刀法简捷地推广了Paule的结果,从而得到了一系列多重Rogers-Ramanujan恒等式. 相似文献
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初文昌 《纯粹数学与应用数学》1993,9(1):1-6
本文提出联系两类组合恒等式的极限方法,据此可二项式系数和项式系数恒等式自然过渡到Abel型系数的组合等式。因此对任一给定的含参量的二项式系数的组合恒等式。这一方法可用于直接证明其至发现相同结构的Abel系数恒等式。 相似文献
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本文将论述通过q-级数互反关系证明经典分拆恒等式的一般方法。应用Carlitz给出的Gould-Hsu反演的q-模拟,作者将建立一个重要的和式变换定理。作为例证:结合Jacobi三重积恒等式及组合计算技巧,给出Rogers-Ra-manujan恒等式一个新的简单推证。 相似文献
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易媛 《纯粹数学与应用数学》1998,14(4):78-84
主要运用初等方法及Riemann Zeta-函数和Dirichlet L-函数的性质研究了一类无穷级数的计算问题,并且给出了一个有趣的恒等式。 相似文献
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关于联系两个单形的几何恒等式及应用 总被引:3,自引:0,他引:3
关于n维欧氏空间E~n中二单形之间的几何关系的研究,一向是距离几何中被关注的课题。如仅就周知的涉及两个二维单形的Neuberg-Pedoe不等式而言,1942年Pedoe给出其第一个证明,此后数十年中,Pedoe和别人又相继提供了许多新的证明,几何的或纯代数的,Pedoe的最近的一个证明发表于1976年,而到1981年又由杨路、张景中将其推广到高维空间。 本文的结果在于给出联系两个单形的一个恒等式,并由此推出了一些新的涉及两个单形的不等式。 相似文献
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Wenchang Chu 《Mathematical Methods in the Applied Sciences》2019,42(6):1831-1843
A new class of twisted cubic q‐series is investigated by means of the modified Abel lemma on summation by parts. Several remarkable summation and transformation formulae are established for both terminating and nonterminating series. 相似文献
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In this paper we give analogues of the Ramanujan functions and nonlinear differential equations for them. Investigating a modular structure of solutions for nonlinear differential systems, we deduce new identities between the Ramanujan and hypergeometric functions. Another result of this paper is a solution of transcendence problems concerning nonlinear systems. 相似文献
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《代数通讯》2013,41(4):1011-1022
ABSTRACT The algebras M a, b (E) ? E and M a+b (E) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984–1987 (see Kemer 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M 1, 1(E) ? E and M 2(E) when the base field is infinite and of characteristic p > 2. The algebra M a, a (E) ? E satisfies certain graded identities that are not satisfied by M 2a (E). In another paper we proved that the algebras M 1, 1(E) and E ? E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities. 相似文献
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Renrong Mao 《Journal of Number Theory》2013,133(11):3678-3702
In 1954, A.O.L. Atkin and H.P.F. Swinnerton-Dyer established the generating functions for rank differences modulo 5 and 7 for partition functions. In this paper, we derive formulas for the generating functions of ranks of partitions modulo 10 and some inequalities between them. 相似文献
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In this paper we have given transformations for the partial mock theta functions of order five and also some identities between these partial mock theta functions analogous to the identities given by Ramanujan. 相似文献
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Wolfram Koepf Mohammad Masjed-Jamei 《Proceedings of the American Mathematical Society》2007,135(11):3599-3606
Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by , which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences.