共查询到17条相似文献,搜索用时 62 毫秒
1.
2.
3.
4.
契贝谢夫多项式的一些恒等式及其斐波纳奇数 总被引:5,自引:0,他引:5
1 引言与结果著名的契贝谢夫多项式 [1]为 Un( x) =12 x2 - 1 [( x + x2 - 1 ) n+1- ( x - x2 - 1 ) n+1].因此 ,Un( x)n!=12 x2 - 1 . 1n![( x + x2 - 1 ) n+1- ( x - x2 - 1 ) n+1], ∞n=0Un( x) /n!. tn =12 x2 - 1 ∞n=01n![( x + x2 - 1 ) n+1- ( x - x2 - 1 ) n+1]tn =12 x2 - 1 [( x + x2 - 1 ) exp( ( x + x2 - 1 ) t) -( x - x2 - 1 ) exp( ( x - x2 - 1 ) t) ]=Φ ( t) .因此 ,Un( x) /n!可由Φ ( t)展开式的系数来确定 .本文中将利用初等方法给出契贝谢夫多项式的一些恒等式及与斐波纳奇数的关系 ,即定理 1及推论 1 .定理 1… 相似文献
5.
苟素 《纺织高校基础科学学报》2011,24(2):250-252,269
Vk∈ N+,l<k≤9,数列{a(k,n)}称作Smarandache kn数字数列,如果该数列中的每一个数都可以分成两部分,那么第二部分是第一部分的k倍,例如3n数字数列{α(3,n)}定义为{13,26,39,412,515,618,721,824,…}.利用初等及组合方法研究Smarandache kn数字数列... 相似文献
6.
关于Fibonacci数的一些恒等式 总被引:3,自引:0,他引:3
杨长恩 《纺织高校基础科学学报》1999,12(4):351-354
研究了Fibonacci数的一些性质,并给出了一类新的恒等式和一些有趣的同余式。 相似文献
7.
利用初等方法研究 Cochrane和的一个算术性质,给出一个有趣的恒等式。 相似文献
8.
9.
韩彬玲 《纺织高校基础科学学报》2012,25(1):71-74
一个自然数n称为三角数,如果n=m(m+1)/2,其中m为任意正整数.三角数的Smarandache连续数列E={Tn}={1,13,136,13 610,1 361 015,136 101 521,13 610 152 128,…},即Tn就是由前n个三角数相继连接起来构成的正整数.利用初等方法以及等比级数的性质研究三角数的Smarandache连续数列E的算术性质,并给出其对数倒数形成的无穷级数的敛散性的一个判别准则. 相似文献
10.
王丹芳 《纺织高校基础科学学报》2015,(2)
为了研究拉盖尔多项式卷积的正交性,运用初等方法以及幂级数的性质得到了拉盖尔多项式卷积 H(x ,k+1,n)的一类恒等式,并运用定义和已知的性质给出这类卷积的一个计算公式,及其正交性的计算公式。对拉盖尔多项式的研究有一定的推动作用。 相似文献
11.
关于Fibonacci数偶次幂的恒等式 总被引:1,自引:1,他引:1
根据Chebyshev多项式和Fibonacci数的关系以及第一类第二类Chebyshev多项式的性质,用初等的方法得到了Fibonacci数偶次幂积和式的计算公式. 相似文献
12.
关于Fibonacci数任意次幂的一些恒等变换 总被引:4,自引:0,他引:4
杨长恩 《纺织高校基础科学学报》2000,13(2):114-118
研究了Fibonacci数任意次幂的一些恒等变换,并得出一些有趣的同余式。 相似文献
13.
甘泉 《纺织高校基础科学学报》2001,14(1):79-80
In this paper,the following two equalities involved with combinatorial numbers are proved:(1 ) nk=0Ck2 k Cn- k2 n- 2 k =4n,n =0 ,1 ,2 ,3,… ,(2 ) nk=012 k + 1 Ck2 k Cn- k2 n- 2 k4n (2 n) !!(2 n + 1 ) !!,n =0 ,1 ,2 ,3,… .1 Proof of the first equalityConsider the power series expansion of function1 / 1 -x,11 -x=(1 -x) - 1/2 =1 + -1 / 21 !(-x) 1 / 2 (-1 / 2 -1 )2 !(-x) 2 +-1 / 2 (-1 / 2 -1 ) (-1 / 2 -2 )3!(-x) 3 +…=1 + 12 x + 3!!4!!x2 + 5 !!6 !!x3+… =… =1 + ∞n=1(2 n -1 ) !!(2 n) !!xn =… 相似文献
14.
《Pedagogy, Culture & Society》2008,16(1):43-55
There is a well-established literature that is concerned with the ways in which teachers construct their professional identities. There is also a great deal of research that has traced shifts in teacher identities across a career trajectory, the life-history approach. In the majority of this work the starting point and the finishing place has focused on the time spent actively engaged in teaching. This article explores teacher identity from another under-researched perspective. That is, what happens to teachers' identities when they no longer work as teachers, when they have perhaps laid down this aspect of their identity, when they have reached their 'end of term'? The purpose of this enquiry is two-fold. First, the intention is to critically explore theoretical constructions of teacher identities; second, the intention is to start to problematise both retirement as disengagement and life-stage approaches to teacher career and identity.
The article is organised as follows. First, I briefly review some of the different ways in which identity is understood and deployed. Then I consider some of the major research into teacher identity, the life-cycle of the teacher and some of the work on 'end-of career' teachers. The second half of the article draws on a small data set to explore the different ways that teachers have invested in their occupational identity, or not. It also charts what happens (to their teacher identities) when this occupation stops. Finally the article considers what those who used to teach can tell us about teacher identity and a job they no longer do. 相似文献
The article is organised as follows. First, I briefly review some of the different ways in which identity is understood and deployed. Then I consider some of the major research into teacher identity, the life-cycle of the teacher and some of the work on 'end-of career' teachers. The second half of the article draws on a small data set to explore the different ways that teachers have invested in their occupational identity, or not. It also charts what happens (to their teacher identities) when this occupation stops. Finally the article considers what those who used to teach can tell us about teacher identity and a job they no longer do. 相似文献
15.
关于Lucas数的计数函数 总被引:2,自引:0,他引:2
王维琼 《纺织高校基础科学学报》2002,15(2):99-101
研究了著名的Lucas数列,并给出其计数函数均值的一个精确的计算公式。 相似文献
16.
17.
李洁 《纺织高校基础科学学报》2005,18(3):207-208,236
对于给定的自然数n和k,若把kn个不同的元素分成k组,每组都有n个不同的元素,这样分组的种数为Ckn^(k)=((kn)!/(n!)^k.研究了这种多组组合数Ckn^(k)在素因数个数函数(包括重数在内)上的值分布性质,并得到了一个有趣的渐近公式. 相似文献