共查询到20条相似文献,搜索用时 218 毫秒
1.
关于包含奇-偶下标第二类契贝谢夫多项式的恒等式 总被引:7,自引:1,他引:7
给出了一类包含偶下标第二类契贝谢夫多项式和一类包含奇下标第二类契贝谢夫多项式求和的递推公式,得到了一些包含偶下标第二类契贝谢夫多项式和奇下标第二类契贝谢夫多项式的恒等式. 相似文献
2.
主要研究勒让德多项式与契贝谢夫多项式之间的关系的性质,利用生成函数和函数级数展开的方法,得出了勒让德多项式与契贝谢夫多项式之间的一个重要关系,这对勒让德多项式与契贝谢夫多项式的研究有一定的推动作用. 相似文献
3.
一些包含契贝谢夫多项式的恒等式 总被引:6,自引:2,他引:4
亢小玉 《纯粹数学与应用数学》2000,16(2):55-57
讨论了著名的契贝射夫多项式的一些性质,并给出了一些有趣的恒等式。 相似文献
4.
5.
6.
通过讨论一类函数的高阶导数 ,建立了一些包含 Hermite-Laguerre多项式的恒等式 ,推广了著名的 Cauchy-Sheehan组合恒等式 . 相似文献
7.
在求函数 y =A·sin(ωx φ)及 y =A·cos(ωx φ)的单调区间时 ,学生往往容易出错 ,特别是在ω <0的情况下 ,尤为突出 .本文介绍一种既保险又快捷的求法 ,解法分三步 .第一步 :求出函数的最小正周期T =2π|ω|;第二步 :寻找一个x0 ,使x =x0 时 ,y值最大 ;图 1 y =Asin(ωx φ)示意图第三步 :写出函数的单调增区间[kT x0 -T2 ,kt x0 ] ,k∈N ;单调减区间 [kT x0 ,kT x0 T2 ] ,k∈N .以上解法 ,请同学们结合图 1就不难理解了 ,关于x0 的求法 ,只须根据A的符号及函数名称 ,令ωx φ =… 相似文献
8.
9.
10.
11.
12.
Dong-mei Jiang 《Applied mathematics and computation》2010,217(8):3898-3902
A new approach is constructed to obtain exact travelling wave solutions for a differential-difference equation by means of the property of the symmetrical Fibonacci sine and cosine function. As its illustration, some explicit and exact travelling wave solutions of Hybrid lattice, discretized mKdV lattice and modified Volterra lattice are obtained by computing the solutions of a lattice introduced by Wadati. 相似文献
13.
Ronald E. Mickens 《Journal of Difference Equations and Applications》2013,19(6):1042-1047
We construct the exact finite difference equation discretizations for the nonlinear differential equations whose solutions are the Jacobi cosine and sine functions. Our derivations clarify and extend previous work done on this topic. 相似文献
14.
Several improvements are made to an algorithm of Higham and Smith for computing the matrix cosine. The original algorithm
scales the matrix by a power of 2 to bring the ∞-norm to 1 or less, evaluates the [8/8] Padé approximant, then uses the double-angle
formula cos (2A)=2cos 2A−I to recover the cosine of the original matrix. The first improvement is to phrase truncation error bounds in terms of ‖A2‖1/2 instead of the (no smaller and potentially much larger quantity) ‖A‖. The second is to choose the degree of the Padé approximant to minimize the computational cost subject to achieving a desired
truncation error. A third improvement is to use an absolute, rather than relative, error criterion in the choice of Padé approximant;
this allows the use of higher degree approximants without worsening an a priori error bound. Our theory and experiments show
that each of these modifications brings a reduction in computational cost. Moreover, because the modifications tend to reduce
the number of double-angle steps they usually result in a more accurate computed cosine in floating point arithmetic. We also
derive an algorithm for computing both cos (A) and sin (A), by adapting the ideas developed for the cosine and intertwining the cosine and sine double angle recurrences.
AMS subject classification 65F30
Numerical Analysis Report 461, Manchester Centre for Computational Mathematics, February 2005.
Gareth I. Hargreaves: This work was supported by an Engineering and Physical Sciences Research Council Ph.D. Studentship.
Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/T08739 and by a
Royal Society–Wolfson Research Merit Award. 相似文献
15.
Gwang Hui Kim 《数学学报(英文版)》2009,25(1):29-38
The aim of this paper is to study the stability problem of the generalized sine functional equations as follows:
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
16.
Using supercharacter theory, we identify the matrices that are diagonalized by the discrete cosine and discrete sine transforms, respectively. Our method affords a combinatorial interpretation for the matrix entries. 相似文献
17.
18.
Nguyen Xuan Thao Hoang Thi Van Anh 《Mathematical Methods in the Applied Sciences》2014,37(15):2308-2319
In this paper, we construct and study a new generalized convolution (f * g)(x) of functions f,g for the Hartley (H1,H2) and the Fourier sine (Fs) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities: We prove the existence of this generalized convolution on different function spaces, such as . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Hainan Ma 《Integral Transforms and Special Functions》2016,27(5):365-370
Liu [An extension of the quintuple product identity and its applications. Pacific J Math. 2010;246:345–390] established a theta function identity. In this paper, we will give an equivalent form of Liu's identity, from which some non-trivial identities on circular summation of theta functions are deduced. 相似文献
20.
George A. Anastassiou 《Semigroup Forum》2008,76(1):149-158
Various L
p
form Opial type inequalities are given for cosine and sine operator functions with applications. 相似文献