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71.
Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s 1ψ1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity
theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application
to sums of three squares.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—33D15
B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency.
A. J. Yee: Research partially supported by a grant from The Number Theory Foundation. 相似文献
72.
Mourad E. H. Ismail 《The Ramanujan Journal》2006,11(3):349-353
We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved
by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and
used to study a generating function for the number of partitions with specified crank.
Research partially supported by NSF grant DMS 99-70865.
2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20 相似文献
73.
The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>
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The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it. 相似文献
74.
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77.
Nikolay Kuznetsov 《Comptes Rendus Mecanique》2004,332(1):73-78
This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements. To cite this article: N. Kuznetsov, C. R. Mecanique 332 (2004). 相似文献
78.
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a recursive structure for certain compound shifted Delaporte mixtures with Borel summands. Our models are introduced in an actuarial context as claim number distributions and are derived only with probabilistic arguments and elementary combinatorial identities. In the actuarial context related compound distributions are of importance as models for the total size of insurance claims for which we present simple recursion formulas of Panjer type. 相似文献
79.
C.J. Read 《Journal of Mathematical Analysis and Applications》2011,381(1):202-217
We show that in every nonzero operator algebra with a contractive approximate identity (or c.a.i.), there is a nonzero operator T such that ‖I−T‖?1. In fact, there is a c.a.i. consisting of operators T with ‖I−2T‖?1. So, the numerical range of the elements of our contractive approximate identity is contained in the closed disk center and radius . This is the necessarily weakened form of the result for C?-algebras, where there is always a contractive approximate identity consisting of operators with 0?T?1 - the numerical range is contained in the real interval [0,1]. So, if an operator algebra has a c.a.i., it must have operators with a “certain amount” of positivity. 相似文献
80.
Feizhi Wang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):827-835
In this paper we study the existence of solutions for nonlinear Klein-Gordon-Maxwell equations coupled with Maxwell’s equations when the nonlinearity exhibits critical growth. We improve some previous existence results in Azzollini et al. (2009) [5], Carrião et al. (2009) [4] and Cassani (2004) [3]. 相似文献