广义Riesz基的双正交特征刻画

本文利用广义双正交序列研究广义Riesz基的等价刻画,得到了算子序列是广义Riesz基当且仅当该算子列是广义完备的广义Bessel序列,且它存在广义双正交序列及这个双正交序列也是广义完备的广义Bessel序列.进一步证明了等价刻画中两个广义Bessel序列的广义完备性条件可以去掉一个(或者任一个),并举例说明了广义双正交,广义完备与广义Bessel条件之间的关系.     

广义完全Bessel序列和广义下半框架条件

研究广义完全Bessel序列和广义下半框架,包括离散和连续两种情形.首先讨论广义完全Bessel序列的分析算子性质;其次建立广义下半框架的充要条件;最后证明广义完全Bessel序列的对偶是广义下半框架.     

一些包含Chebyshev多项式和Stirling数的恒等式

利用初等方法研究Chebyshev多项式的性质,建立了广义第二类Chebyshev多项式的一个显明公式,并得到了一些包含第一类Chebyshev多项式,第一类Stirling数和Lucas数的恒等式.     

第二类Chebyshev多项式系数的绝对值和的卷积

本文主要的目的是利用广义Fibonacci多项式的生成函数及其偏导数来研究第二类Cheby-shev多项式卷积的计算,并给出—个有趣的计算公式.     

广义的k阶Fibonacci-Jacobsthal序列及其性质

定义了一类广义的k阶Fibonacci-Jacobsthal序列,并给出了第四个初值条件.借助矩阵的方法得到了Jacobsthal序列与Jacobsthal-Lucas序列的关系,广义k阶Fibonacci-Jacobsthal序列与Jacobsthal序列,Fibonacci序列的关系,同时给出了k阶Fibonacc...     

局部广义高斯序列与广义线性过程

本文对局部广义高斯序列得到了ｒ阶绝对矩的上界不等式，进而对由其生成的广义线性过程｛Ｘｎ｝给出了ａ．ｓ．收敛的充分条件。     

NA序列广义Jamison型加权和的几乎处收敛性

本文从随机变量序列广义Jamison型加权和的一个系数指标函数自身性质出发，讨论了广义Jamison型加权和的强稳定性，避免了控制函数的引入，进一步还得到了更一般的NA序列广义Jamison型加权和的几乎处处收敛的条件，并将前人的若干结论包含为特例。     

局部广义高斯序列的若干新结果

给出了局部广义高斯序列部分和的一类绝对矩不等式及大偏差,并利用这些不等式证明了局部广义高斯序列的大数定律,同时建立了局部广义高斯序列的重对数收敛速度.     

广义Rudin－Shapiro函数及其性质

为获得动力系统的高阶谱数［１２］，Ｑｕｅｆｆｅｌｅｃ引入了广义（ｑ阶ｑ≥３）Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列｛ｒｋ｝，起关键作用的指数和的不等式为：回一１其中常数Ｃ取值为，本文对广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列进行了进一步研究，引入了广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ函数，将以上系数Ｃ改进为，并证明了是Ｒ上一个连续但几乎处处不可微的周期为１的函数，取值于与之间，使得     

几何序列与拟广义几何序列的互相关函数

本文构造了一类与几何序列的互相关特性非常好的新序列－拟广义几何序列。     

Dedekind和及第一类Chebyshev多项式

本文利用分析方法、Dedekind和及第一类Chebyshev多项式的算术性质,研究了一类关于Dedekind和及第一类Chebyshev多项式混合均值的渐近估计问题,并得到了一个较强的渐近公式.     

三对角行列式与Chebyshev多项式

给出了三对角行列式的几种算法,利用三对角行列式证明了两类Chebyshev多项式的几种显式.     

Some new Chebyshev spaces

In this note we see another circumstance where Chebyshev polynomials play a significant role. In particular, we present some new extended Chebyshev spaces that arise in the asymptotic stability of the zero solution of first order linear delay differential equations with m commensurate delays where a_j,j=0,…,m, are constants and τ>0 is constant.     

第一类双变量Chebyshev多项式的最小零偏差性质研究

利用Rivlin和Shapiro提出的符号理论,证明了文献[10]中提出的第一类双变量Chebyshev多项式恰为所谓的Steiner区域上具有特殊首项的最小零偏差多项式,并由此导出了几类具有一定代数精度的数值积分公式.     

On the restricted Chebyshev–Boubaker polynomials

Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev–Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and we study certain central sequences defined by their coefficient arrays. We give an integral representation for their moments, and we show that the Hankel transforms of these moments have a simple form. We show that the (sequence) Hankel transform of the row sums of the corresponding moment matrix is defined by a family of polynomials closely related to the Chebyshev polynomials of the second kind, and that these row sums are in fact the moments of another family of orthogonal polynomials.     

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x ²ⁿ + y ²ⁿ , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.     

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

Orthogonal polynomials satisfy a recurrence relation of order two defined by two sequences of coefficients. If we modify one of these recurrence coefficients at a certain order, we obtain the so-called perturbed orthogonal sequence. In this work, we analyse perturbed Chebyshev polynomials of second kind and we deal with the problem of finding the connection coefficients that allow us to write the perturbed sequence in terms of the original one and in terms of the canonical basis. From the connection coefficients obtained, we derive some results about zeros at the origin. The analysis is valid for arbitrary order of perturbation.     

Algorithms for the integration and derivation of Chebyshev series

General formulas for the mth integral and derivative of a Chebyshev polynomial of the first or second kind are presented. The result is expressed as a finite series of the same kind of Chebyshev polynomials. These formulas permit to accelerate the determination of such integrals or derivatives. Besides, it is presented formulas for the mth integral and derivative of finite Chebyshev series and a numerical algorithm for the direct evaluation of the mth derivative of such a series.     

关于勒让德多项式与契贝谢夫多项式间的关系

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．