Asymptotics for Laguerre-Sobolev type orthogonal polynomials modified within their oscillatory regime Articles uri icon

publication date

  • June 2014

start page

  • 260

end page

  • 272

volume

  • 236

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

abstract

  • In this paper we consider sequences of polynomials orthogonal with respect to the discrete Sobolev inner productf,gS=0f(x)g(x) xalfae-xdx+F(c)AG(c)t,alfa>-1,where f and g are polynomials with real coefficients, AR(2,2) and the vectors F(c),G(c) areA=M00N,F(c)=(f(c),f′(c))andG(c)=(g(c), g′(c)),respectively,with M,NR+ and the mass point c is located inside the oscillatory region for the classical Laguerre polynomials. We focus our attention on the representation of these polynomials in terms of classical Laguerre polynomials and we analyze the behavior of the coefficients of the corresponding five-term recurrence relation when the degree of the polynomials is large enough. Also, the outer relative asymptotics of the Laguerre-Sobolev type with respect to the Laguerre polynomials is analyzed.

keywords

  • asymptotics, discrete sobolev polynomials, laguerre polynomials; orthogonal polynomials, orthogonal functions, asymptotics, laguerre polynomial, orthogonal polynomial, oscillatory regimes, oscillatory regions, real coefficients, recurrence relations, sobolev, polynomials