共查询到20条相似文献,搜索用时 15 毫秒
1.
《Indagationes Mathematicae (Proceedings)》1982,85(4):415-422
Among polynomials in several variables of given form, the Laguerre and Hermite polynomials are recovered. This is obtained by requiring that the polynomials in several variables satisfy known properties characterizing the classical polynomials.Analogous characterizations of the Meixner polynomials are likewise determined. These are based on the characteristic properties of the Meixner polynomials recently established.All new properties generalize the previous ones. 相似文献
2.
《Journal of Computational and Applied Mathematics》1999,103(2):323-335
An explicit representation of the co-recursive associated Meixner polynomials is given in terms of hypergeometric functions. This representation allows to derive a generating function, the Stieltjes transform of the orthogonality measure and the fourth-order difference equation verified by these polynomials. Special attention is given to some simple limiting cases ocurring in the solution of the Chapman-Kolmogorov equation of linear birth and death processes. 相似文献
3.
Jean Letessier André Ronveaux Galliano Valent 《Journal of Computational and Applied Mathematics》1996
An explicit representation of the associated Meixner polynomials (with a real association parameter γ?0) is given in terms of hypergeometric functions. This representation allows to derive the fourth-order difference equation verified by these polynomials. Appropriate limits give the fourth-order difference equation for the associated Charlier polynomials and the fourth-order differential equations for the associated Laguerre and Hermite polynomials. 相似文献
4.
V.K. Srinivasan 《International Journal of Mathematical Education in Science & Technology》2013,44(2):283-284
The square notation for proportions is used to investigate a question arising from the theory of statistics. 相似文献
5.
Holger Dette 《Proceedings of the American Mathematical Society》2001,129(6):1805-1815
For a birth and death chain on the nonnegative integers, integral representations for first return probabilities are derived. While the integral representations for ordinary transition probabilities given by Karlin and McGregor (1959) involve a system of random walk polynomials and the corresponding measure of orthogonality, the formulas for the first return probabilities are based on the corresponding systems of associated orthogonal polynomials. Moreover, while the moments of the measure corresponding to the random walk polynomials give the ordinary return probabilities to the origin, the moments of the measure corresponding to the associated polynomials give the first return probabilities to the origin.
As a by-product we obtain a new characterization in terms of canonical moments for the measure of orthogonality corresponding to the first associated orthogonal polynomials. The results are illustrated by several examples.
6.
Li-Chien Shen 《Proceedings of the American Mathematical Society》2001,129(3):873-879
Using the well-known fact that the Fourier transform is unitary, we obtain a class of orthogonal polynomials on the unit circle from the Fourier transform of the Laguerre polynomials (with suitable weights attached). Some related extremal problems which arise naturally in this setting are investigated.
7.
We study the asymptotic behavior of multiple Meixner polynomials of first and second kind, respectively [6]. We use an algebraic function formulation for the solution of the equilibrium problem with constraint to describe their zero distribution. Moreover, analyzing the limiting behavior of the coefficients of the recurrence relations for Multiple Meixner polynomials we obtain the main term of their asymptotics. 相似文献
8.
Stanis?aw Lewanowicz 《Journal of Computational and Applied Mathematics》1997,80(2):351-358
Three equivalent forms of the fourth-order difference equation obeyed by the associated Meixner polynomials (with a nonnegative real association parameter) are derived from a refinement of a recent result due to Letessier et al. (1996). 相似文献
9.
We investigate the zeros of a family of hypergeometric polynomials $M_n(x;\beta ,c)=(\beta )_n\,{}_2F_1(-n,-x;\beta ;1-\frac{1}{c})$ , $n\in \mathbb N ,$ known as Meixner polynomials, that are orthogonal on $(0,\infty )$ with respect to a discrete measure for $\beta >0$ and $0<c<1.$ When $\beta =-N$ , $N\in \mathbb N $ and $c=\frac{p}{p-1}$ , the polynomials $K_n(x;p,N)=(-N)_n\,{}_2F_1(-n,-x;-N;\frac{1}{p})$ , $n=0,1,\ldots , N$ , $0<p<1$ are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polynomials $M_n(x;\beta ,c)$ , $c<0$ and $n<1-\beta $ , the quasi-orthogonal polynomials $M_n(x;\beta ,c)$ , $-k<\beta <-k+1$ , $k=1,\ldots ,n-1$ and $0<c<1$ or $c>1,$ as well as the polynomials $K_{n}(x;p,N)$ with non-Hermitian orthogonality for $0<p<1$ and $n=N+1,N+2,\ldots $ . We also show that the polynomials $M_n(x;\beta ,c)$ , $\beta \in \mathbb R $ are real-rooted when $c\rightarrow 0$ . 相似文献
10.
We give a probabilistic interpretation of the associated Jacobi polynomials, which can be constructed from the three-term recurrence relation for the classical Jacobi polynomials by shifting the integer index n by a real number t. Under certain restrictions, this will give rise to a doubly infinite tridiagonal stochastic matrix, which can be interpreted as the one-step transition probability matrix of a discrete-time bilateral birth–death chain with state space on . We also study the unique UL and LU stochastic factorizations of the transition probability matrix, as well as the discrete Darboux transformations and corresponding spectral matrices. Finally, we use all these results to provide an urn model on the integers for the associated Jacobi polynomials. 相似文献
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12.
Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials
The authors continue to study generalized coherent states for oscillator-like systems connected with a given family of orthogonal
polynomials. In this work, we consider oscillators connected with Meixner and Meixner— Pollaczek polynomials and define generalized
coherent states for these oscillators. A completeness condition for these states is proved by solution of a related classical
moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic
model of a linear harmonic oscillator can be treated as the linearization of a quadratic Hamiltonian, which arises naturally
in our formalism. Bibliography: 56 titles.
The authors dedicate this work to their friend and colleague P. P. Kulish on the occasion of his 60th birthday
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 66–93. 相似文献
13.
M. Sh. Dzhamalov 《Mathematical Notes》1997,62(4):519-520
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We give an analog of exceptional polynomials in the matrix-valued setting by considering suitable factorizations of a given second-order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence are discussed in detail. We give an example of matrix-valued exceptional Laguerre polynomials of arbitrary size. 相似文献
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17.
Bruno Gabutti 《Journal of Mathematical Analysis and Applications》1983,95(1):265-277
A new characterization of the Meixner polynomials is established. It is based on the solution of a problem related to a previous result concerning the Laguerre polynomials. Solutions of analogous problems provide characteristic properties of the Laguerre and Hermite polynomials. These properties, which are derived from the two-variable polynomials, generalize, in turn, the previous ones. 相似文献
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The Ramanujan Journal - Let $$D_h$$ , $$E_k$$ and $$F_{alpha }$$ be sets of size $$h,k,alpha $$ respectively, with $$k le h$$ . We define a strongly widened derangement to be a permutation of... 相似文献
20.
Richard Askey Mourad E.H Ismail Tom Koornwinder 《Journal of Combinatorial Theory, Series A》1978,25(3):277-287
The connection between integrals of products of Laguerre polynomials, power series coefficients of certain rational functions of several variables, and certain numbers of weighted permutation problems is investigated. A combinatorial proof of our main result would be very desirable since this could lead the way to more general result, q-analogs, and perhaps even a q-analog of MacMahon's Master Theorem. 相似文献