Weideman公式的证明  

The proof of Weideman conjecture

作　　者：林谷佳 LING Gujia(School of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《周口师范学院学报》2018年第5期1-6,共6页Journal of Zhoukou Normal University

摘　　要：利用Dougall-Dixon求和公式,将公式中的a,b,c进行含参赋值,再通过恒等变换,使其化为一个关于二项系数的恒等式,通过对所得恒等式进行求导,得到一系列关于调和级数与二项系数的恒等式,所得的恒等式在组合数学方面有所应用,利用所得恒等式的其中之三,证明了著名的Weideman公式.Relying on Dougall-Dixon summation theorem , l assign parameters replacements to a, b, c, d of the theorein . Then , by means of identity transformation , the equation is transformed into an identity of binomial coefficients. By applying the derivation opcrator to the identity, I get a series of identities with harmonic numbers and binomial coefficients, which are applied to combinatorial mathematics. Using three of the identities, I get the proof of Weideman conjecture.

关 键 词：Weideman公式 Dougall-Dixon公式 二项式系数 超几何级数 调和级数 

分 类 号：O157.2[理学—数学]