Laguerre Polynomials, Weighted Derangements, and Positivity
نویسندگان
چکیده
A calculation of the linearization coefficients of the (generalized) Laguerre polynomials L")(x) is proposed by means of analytic and combinatorial methods. This paper extends to the case of an arbitrary a a combinatoric and analytic result due to Askey, Ismail, and Koornwinder and Even and Gillis. Theorem (/-extension) AMS(MOS) subject classifications. 33A65, 05A 15 1. Introduction. Let (p,,(x)) be a sequence of polynomials, orthogonal with respect to a weight function w. One of the aspects of the linearization of the product of the
منابع مشابه
Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials
The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...
متن کاملApplication of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
In this study, an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials. Properties of these polynomials and operational matrix of integration are first presented. These properties are then used to transform the integral equation to a matrix equation which corresponds t...
متن کاملDerangements and asymptotics of Laplace transforms of polynomials
We describe the behavior as n → ∞ of the Laplace transforms of P, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equival...
متن کامل2 1 Ja n 20 04 Derangements and asymptotics of Laplace transforms of polynomials
We describe the behavior as n → ∞ of the Laplace transforms of Pn, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equiva...
متن کاملA Stable Solution of Time Domain Electric Field Integral Equation Using Weighted Laguerre Polynomials
In this article, we propose a new stable solution for the time domain electric field integral equation (TD-EFIE) for arbitrarily shaped conducting structures, which utilizes weighted Laguerre polynomials as temporal basis functions, which means that the unknown surface currents are expanded by these basis functions. The proposed algorithm is based on the Galerkin’s scheme that involves separate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 1 شماره
صفحات -
تاریخ انتشار 1988