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11.
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
12.
We present two infinite families of generalized Lambert seriesidentities, and deduce several known identities from them. Theyinclude an identity due to M. Jackson, a corollary of Ramanujan's11-summation formula, and a recent identity of G. E. Andrews,R. P. Lewis and Z.-G. Liu. 2000 Mathematics Subject Classification33D15, 11D85. 相似文献
13.
A q, z-analogue and of polynomials of binomial type gives rise to a bibasic extension of the q-Saalschütz identity. 相似文献
14.
We apply multidimensional matrix inversions to multiple basic hypergeometric summation theorems to derive several multiple (q-)series identities which themselves do not belong to the hierarchy of (basic) hypergeometric series. Among these are A terminating and nonterminating q-Abel and q-Rothe summations. Furthermore, we derive some identities of another type which appear to be new already in the one-dimensional case. 相似文献
15.
q-Analogues of the coefficients of xa in the expansion of
j=1
N
(1 + x + + xj)Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the q-supernomial coefficients are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson-fermion-type, based on the continued fraction expansion of p/k and involving the q-supernomial coefficients, are proven. These include polynomial analogues of the Andrews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters. 相似文献
16.
For primes we obtain a simple formula for p(N) (mod ) as a weighted sum over -square affine partitions of N. When {3,5,7,11}, the weights are explicit divisor functions. The Ramanujan congruences modulo 5, 7, 11, 25, 49, and 121 follow immediately from these formulae. 相似文献
17.
The Rogers L-function
satisfies the functional equation
.From this we derive several other such equations, including Euler's identity L(x)+L(1-x)=L(1) and various identities arising from summation and transformation formulas for basic hypergeometric series. We also obtain some new equations of the form
where is algebraic and the c
k are integers. 相似文献
18.
19.
Remy Y. Denis S. N. Singh S. P. Singh 《Journal of Computational and Applied Mathematics》2003,160(1-2):95-101
In this paper, we have established certain transformations of basic hypergeometric series with more than one base. Some of these lead to the relationship between product of two q-series. These results, in turn, lead to very interesting transformations of bi-basic and poly-basic q-series. A few of the results which are representative of the many results obtained are presented in this article. 相似文献
20.
In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included. 相似文献