共查询到20条相似文献,搜索用时 15 毫秒
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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. 相似文献
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Refik Keskin 《International Journal of Mathematical Education in Science & Technology》2013,44(3):379-387
The aim of this article is to characterize the 2 × 2 matrices X satisfying X 2 = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. 相似文献
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Jishe Feng 《Applied mathematics and computation》2011,217(12):5978-5981
In this paper, using the method of Laplace expansion to evaluate the determinant tridiagonal matrices, we construct a kind of determinants to give new proof of the Fibonacci identities. 相似文献
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The Legendre–Stirling numbers are the coefficients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejohn gave a combinatorial interpretation of the Legendre–Stirling numbers. In this paper, we establish several properties of the Legendre–Stirling numbers; as with the Stirling numbers of the second kind, they have interesting generating functions and recurrence relations. Moreover, there are some surprising and intriguing results relating these numbers to some classical results in algebraic number theory. 相似文献
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Stefan Stanimirovi? 《Applied mathematics and computation》2011,217(22):9122-9132
In this paper we use the Catalan matrix power as a tool for deriving identities involving Catalan numbers and hypergeometric functions. For that purpose, we extend earlier investigated relations between the Catalan matrix and the Pascal matrix by inserting the Catalan matrix power and particulary the squared Catalan matrix in those relations. We also pay attention to some relations between Catalan matrix powers of different degrees, which allows us to derive the simplification formula for hypergeometric function 3F2, as well as the simplification formula for the product of the Catalan number and the hypergeometric function 3F2. Some identities involving Catalan numbers, proved by the non-matrix approach, are also given. 相似文献
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通过计算两个广义的范德蒙(Vandermonde)行列式,得到了第一类无符号Stirling数和第二类Stirling数的一种新的表示方法:用行列式来表示. 相似文献
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A. Plaza S. Falcón 《International Journal of Mathematical Education in Science & Technology》2013,44(4):563-566
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. 相似文献
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Stefan Stanimirovi Predrag Stanimirovi Marko Miladinovi Aleksandar Ili 《Applied mathematics and computation》2009,215(2):796-805
We introduce the notion of the Catalan matrix whose non-zero elements are expressions which contain the Catalan numbers arranged into a lower triangular Toeplitz matrix. Inverse of the Catalan matrix is derived. Correlations between the matrix and the generalized Pascal matrix are considered. Some combinatorial identities involving Catalan numbers, binomial coefficients and the generalized hypergeometric function are derived using these correlations. Moreover, an additional explicit representation of the Catalan number, as well as an explicit representation of the sum of the first m Catalan numbers are given. 相似文献
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In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004. 相似文献
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Wayne A. Johnson 《Discrete Mathematics》2018,341(5):1237-1243
We consider the exponential generating function whose coefficients encode the dimensions of irreducible highest weight representations which lie on a given ray in the dominant chamber of the weight lattice. This formal power series can be considered as an exponential version of the Hilbert series of a flag variety. In this context, we compute a simple closed form for the exponential generating function in terms of finitely many differential operators and the Stirling polynomials. We prove that this series converges to a product of a rational polynomial and an exponential, and that, by summing the constant term and linear coefficient of this polynomial, we recover the dimension of the representation. 相似文献
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Stefan De Wannemacker 《Mathematische Nachrichten》2007,280(11):1257-1267
We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non‐vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2‐adic valuation of Stirling numbers of the second kind. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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第二类Stirling数的一个公式 总被引:1,自引:0,他引:1
In this paper, We propose and prove the following equation, where is a Stirling number of the second kind, when n≥3 is given. 相似文献
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In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, based on the matrix representations, various identities are derived. 相似文献
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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
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In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization
of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.
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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 aj,j=0,…,m, are constants and τ>0 is constant. 相似文献