Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4619323 | Journal of Mathematical Analysis and Applications | 2010 | 10 Pages |
Abstract
Denote by xn,kM,N(α), k=1,…,nk=1,…,n, the zeros of the Laguerre–Sobolev-type polynomials Ln(α,M,N)(x) orthogonal with respect to the inner product〈p,q〉=1Γ(α+1)∫0∞p(x)q(x)xαe−xdx+Mp(0)q(0)+Np′(0)q′(0), where α>−1α>−1, M⩾0M⩾0 and N⩾0N⩾0. We prove that xn,kM,N(α) interlace with the zeros of Laguerre orthogonal polynomials Ln(α)(x) and establish monotonicity with respect to the parameters M and N of xn,kM,0(α) and xn,k0,N(α). Moreover, we find N0N0 such that xn,nM,N(α)<0 for all N>N0N>N0, where xn,nM,N(α) is the smallest zero of Ln(α,M,N)(x). Further, we present monotonicity and asymptotic relations of certain functions involving xn,kM,0(α) and xn,k0,N(α).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Dimitar K. Dimitrov, Francisco Marcellán, Fernando R. Rafaeli,