共查询到20条相似文献,搜索用时 78 毫秒
1.
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
2.
3.
4.
Bernoulli多项式和Euler多项式的关系 总被引:20,自引:1,他引:20
雒秋明 《数学的实践与认识》2003,33(3):119-122
本文给出了 Bernoulli- Euler数之间的关系和 Bernoulli- Euler多项式之间的关系 ,从而深化和补充了有关文献中的相关结果 . 相似文献
5.
6.
给出四种方法,分别根据特征多项式的性质,多项式根与系数之间的关系以及对称多项式的知识,k次本原单位根,特征多项式的伴侣阵,可在矩阵的特征多项式已知的情况下确定其矩阵方幂的特征多项式. 相似文献
7.
8.
9.
讨论了 Fibonacci数与 Legendre多项式之间的关系 ,得到了一些有趣的恒等式 . 相似文献
10.
Genocchi积分多项式及其性质 总被引:3,自引:0,他引:3
本文研究了Genocchi积分多项式的性质.利用生成函数的方法,得到了Genocchi积分多项式的一些组合恒等式,揭示了Genocchi积分多项式和Genocchi多项式、Bernoulli多项式、Genocchi数、Bernoulli数、Euler数之间的关系. 相似文献
11.
Arturo A. Z. Zavala Heleno Bolfarine Mário de Castro 《Annals of the Institute of Statistical Mathematics》2007,59(3):515-530
The paper concentrates on consistent estimation and testing in functional polynomial measurement errors models with known
heterogeneous variances. We rest on the corrected score methodology which allows the derivation of consistent and asymptotically
normal estimators for line parameters and also consistent estimators for the asymptotic covariance matrix. Hence, Wald and
score type statistics can be proposed for testing the hypothesis of a reduced linear relationship, for example, with asymptotic
chi-square distribution which guarantees correct asymptotic significance levels. Results of small scale simulation studies
are reported to illustrate the agreement between theoretical and empirical distributions of the test statistics studied. An
application to a real data set is also presented. 相似文献
12.
We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depends on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros. 相似文献
13.
A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented,with respect to the polynomial degree.The domains of uniformity are described in certain phase variables.A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation.Global asymptotic approximations are obtained in terms of the Airy function.The system of Hermite polynomials is used as an illustration. 相似文献
14.
Charles A. Micchelli Jianzhong Wang Yi Wang 《Advances in Computational Mathematics》2013,38(3):601-622
In this paper we provide information about the asymptotic properties of polynomial filters which approximate the ideal filter. In particular, we study this problem in the special case of polynomial halfband filters. Specifically we estimate the error between a polynomial filter and an ideal filter and show that the error decays exponentially fast. For the special case of polynomial halfband filters, our n-th root asymptotic error estimates are sharp. 相似文献
15.
We apply polynomial techniques to investigate the structure of spherical designs in an asymptotic process with fixed odd strength while the dimension and odd cardinality tend to infinity in a certain relation. Our bounds for the extreme inner products of special points in such designs allow new lower bounds on the minimum possible odd cardinality. 相似文献
16.
陈协彬 《数学物理学报(A辑)》2003,23(1):65-76
设G是路或圈的笛卡尔乘积图,t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式,并考虑了t(G)的线性递归关系及渐近性态. 相似文献
17.
四元数矩阵理论中的几个概念间的关系 总被引:17,自引:0,他引:17
本文指出并改正文[1]中的错误,给出弱特征多项式[2]与重特征多项式[3]间的显式关系,同时也给出行列式[2]与重行列式[4]间的显式关系,最后讨论了左特征值、右特征值、特征值和特征根之间的关系及最小多项式与弱特征多项式根之间的关系. 相似文献
18.
Anna Valette-Stasica 《Topology and its Applications》2007,154(2):443-448
Using algebraically constructible functions we give a generically effective method to detect asymptotic values of polynomial mappings with finite fibers defined on the real plane. By asymptotic variety we mean the set of points at which the polynomial mapping fails to be proper. 相似文献
19.
Ronen Peretz 《Israel Journal of Mathematics》1998,105(1):1-59
The aim of this paper is to develop a theory for the asymptotic behavior of polynomials and of polynomial maps overR and overC and to apply it to the Jacobian conjecture. This theory gives a unified frame for some results on polynomial maps that were
not related before.
A well known theorem of J. Hadamard gives a necessary and sufficient condition on a local diffeomorphismf: R
n
→R
n
to be a global diffeomorphism. In order to show thatf is a global diffeomorphism it suffices to exclude the existence of asymptotic values forf.
The real Jacobian conjecture was shown to be false by S. Pinchuk. Our first application is to understand his construction
within the general theory of asymptotic values of polynomial maps and prove that there is no such counterexample for the Jacobian
conjecture overC. In a second application we reprove a theorem of Jeffrey Lang which gives an equivalent formulation of the Jacobian conjecture
in terms of Newton polygons. This generalizes a result of Abhyankar. A third application is another equivalent formulation
of the Jacobian conjecture in terms of finiteness of certain polynomial rings withinC[U, V].
The theory has a geometrical aspect: we define and develop the theory of etale exotic surfaces. The simplest such surface
corresponds to Pinchuk's construction in the real case. In fact, we prove one more equivalent formulation of the Jacobian
conjecture using etale exotic surfaces. We consider polynomial vector fields on etale exotic surfaces and explore their properties
in relation to the Jacobian conjecture.
In another application we give the structure of the real variety of the asymptotic values of a polynomial mapf: R
2
→R
2
. 相似文献
20.
Uniform asymptotic formulas are obtained for the Stieltjes-Wigert polynomial, the q−1-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity. In these formulas, the q-Airy polynomial, defined by truncating the q-Airy function, plays a significant role. While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero, the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side. The last two special functions are involved in the local asymptotic formulas of the q-orthogonal polynomials. It seems therefore reasonable to expect that the q-Airy polynomial will play an important role in the asymptotic theory of the q-orthogonal polynomials. 相似文献