A generating function for Laguerre-Sobolev orthogonal polynomials
نویسندگان
چکیده
Let fSng denote the sequence of polynomials orthogonal with respect to the Sobolev inner product
منابع مشابه
Connection coefficients for Laguerre–Sobolev orthogonal polynomials
Laguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form 〈p,q〉S = ∫∞ 0 p(x)q(x)x αe−x dx + λ∫∞ 0 p′(x)q′(x)dμ(x), where α > −1, λ 0, and p,q ∈ P, the linear space of polynomials with real coefficients. If dμ(x) = xαe−x dx, the corresponding sequence of monic orthogonal polynomials {Q n (x)} has been studied by Marcellán et al. (J. Comput. Appl. Math. 71 (1996) 24...
متن کاملDifferential equations for discrete Laguerre-Sobolev orthogonal polynomials
The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre–Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that they are eigenfunctions of a differential operator (which will be explicitly constructed). Moreover,...
متن کاملVarying discrete Laguerre-Sobolev orthogonal polynomials: Asymptotic behavior and zeros
We consider a varying discrete Sobolev inner product involving the Laguerre weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and of their zeros. We are interested in Mehler–Heine type formulas because they describe the asymptotic differences between these Sobolev orthogonal polynomials and the classical Laguerre polynomials. Moreover, they give u...
متن کاملHIGHER ORDER MATCHING POLYNOMIALS AND d-ORTHOGONALITY
We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order matching polynomial corresponds to coverings by paths. Several families of classical orthogonal polynomials—the Chebyshev, Hermite, and Laguerre poly...
متن کاملAsymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Laguerre Type
Let Snn denote a sequence of polynomials orthogonal with respect to the Sobolev inner product f; gS = ∫ f xgxdψ0x + λ ∫ f xgxdψ1x; where λ > 0 and dψ0; dψ1 is a so-called coherent pair with at least one of the measures dψ0 or dψ1 a Laguerre measure. We investigate the asymptotic behaviour of Snx outside the supports of dψ0 and dψ1, and n→+∞. © 2000 Academic Press
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:
- Journal of Approximation Theory
دوره 120 شماره
صفحات -
تاریخ انتشار 2003