Inner products involving q-differences:: the little q-Laguerre-Sobolev polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:118

Article

Area, I ; Godoy, E ; Marcellán, F ; Moreno-Balcázar, JJ

关键词: orthogonal polynomials;    Sobolev orthogonal polynomials;    little q-Laguerre polynomials;   

DOI  :  10.1016/S0377-0427(00)00278-8

来源: Elsevier

【 摘 要 】

In this paper, polynomials which are orthogonal with respect to the inner product (p,r)s =Sigma(k=0)(infinity) p(q(k))r(q(k)) (aq)(k)(aq;q)infinity/(q;q)k + lambda Sigma(k=0)(infinity)(D(q)p)(q(k))(D(q)r)(q(k))(aq)(k) (aq;q)infinity/(q;q)k, where D-q is the q-difference operator, lambda greater than or equal to 0, 0 < q < 1 and 0 < aq < 1 are studied. For these polynomials, algebraic properties and q-difference equations are obtained as well as their relation with the monic little q-Laguerre polynomials. Some properties about the zeros of these polynomials are also deduced. Finally, the relative asymptotics {Q(n)(x)/p(n)(x; a/q)}(n) on compact subsets of C \ [0, 1] is given, where Q(n)(x) is the nth degree monic orthogonal polynomial with respect to the above inner product and p,(n; alg) denotes the monic little q-Laguerre polynomial of degree n. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: primary 33C25; secondary 33D45.

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