# Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics > 1997 > 81 > 2 > 217-227

_{n}(x), orthogonal with respect to the inner product (f,g)s = ∫ f(x)g(x)dμ

_{1}(x) + λ ∫ f (x)g (x)dμ

_{2}(x), λ>0, with x outside of the support of the measure μ

_{2}. We assume that μ

_{1}and μ

_{2}are symmetric and compactly supported measures on R satisfying a coherence condition...

Journal of Computational and Applied Mathematics > 1997 > 81 > 2 > 211-216

^{1}

_{-}

_{1}f(x)g(x(1 - x

^{2})

^{α}

^{-}

^{1}

^{2}dx with α > - 12 and λ > 0. The asymptotics of the zeros and norms of these polynomials are also established.

Journal of Computational and Applied Mathematics > 1997 > 82 > 1-2 > 59-78

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 449-461

Journal of Computational and Applied Mathematics > 2001 > 127 > 1-2 > 297-315

_{n}on K with respect to the L

_{q}(μ)-norm, q [1,~), then zero is also a best approximation to f T on T

^{-}

^{1}(K) with respect to the L

_{q}(μ

^{T})-norm, where μ

^{T}arises from μ by the transformation T. In particular, μ ...

Journal of Computational and Applied Mathematics > 2001 > 127 > 1-2 > 255-266

Journal of Computational and Applied Mathematics > 2001 > 133 > 1-2 > 141-150

_{n}be the polynomials orthogonal with respect to the Sobolev inner product(f,g)

_{S}=∫fgdμ

_{0}+∫f'g'dμ

_{1},being (μ

_{0},μ

_{1}) a coherent pair where one of the measures is the Hermite measure. The outer relative asymptotics for Q

_{n}with respect to Hermite polynomials are found. On the other hand, we consider the Sobolev scaled polynomials and...

Journal of Computational and Applied Mathematics > 2002 > 146 > 2 > 361-372

_{s}=∫02πf(e

^{i}

^{θ})g(e

^{i}

^{θ})|B

_{h}(e

^{i}

^{θ})|

^{2}dθ2π+1λ∫02πf'(e

^{i}

^{@}q)g'(e

^{i}

^{θ})dθ2π,z=e

^{i}

^{θ},where B

_{h}(z) is a complex polynomial of degree h, dθ/2π is the normalized Lebesgue measure and λ...

Journal of Computational and Applied Mathematics > 2003 > 150 > 1 > 25-35

_{S}=∫f(x)g(x)dμ

_{0}(x)+λ∫f'(x)g'(x)dμ

_{1}(x),λ>0,with (μ

_{0},μ

_{1}) being a symmetrically coherent pair of measures with unbounded support. Denote by Q

_{n}the orthogonal polynomials with respect to (1) and they are so-called Hermite-Sobolev orthogonal polynomials. We give a Mehler-Heine-type formula for...

Journal of Computational and Applied Mathematics > 2003 > 151 > 2 > 297-306

_{p}(a,z), which coincides with the familiar normalised function Q(a,z)=Γ(a,z)/Γ(a) when the integer parameter p=1. It is shown that the large-z asymptotics of Q

_{p}(a,z) in the sector |argz|<πp consists of p exponential expansions. In Re(z)>0, all these expansions are recessive at infinity and form a sequence of increasingly...

Journal of Computational and Applied Mathematics > 2003 > 157 > 2 > 297-308

_{N}(x;p)=

_{n}

_{=}

_{0}

^{N}

^{-}

^{1}exp(πixn

^{p}) and T

_{0}=T

_{0}(x;N,p)=

_{n}

_{=}

_{1}

^{~}e

^{-}

^{n}

^{/}

^{N}exp(πixN

^{p}e

^{-}

^{p}

^{n}

^{/}

^{N}), where x>=0 and p>0, is investigated. It is demonstrated that there is an asymptotic connection as N->~ which is found...

Journal of Computational and Applied Mathematics > 2004 > 167 > 2 > 321-343

^{z}

^{p}

^{(}

^{t}

^{)}f(t)dt(|z|->~)to complex values of the variable z. The integration contour...

Journal of Computational and Applied Mathematics > 2004 > 167 > 2 > 293-319

^{x}

^{p}

^{(}

^{t}

^{)}f(t)dt(x->~),where, for simplicity, in this paper x is restricted to be a positive real variable. The integration path C can be taken over both finite and semi-infinite intervals in the complex plane. In general, these expansions take the form...

Journal of Computational and Applied Mathematics > 2005 > 178 > 1-2 > 21-36

Journal of Computational and Applied Mathematics > 2005 > 178 > 1-2 > 465-471

Journal of Computational and Applied Mathematics > 2005 > 179 > 1-2 > 289-301

Journal of Computational and Applied Mathematics > 2005 > 180 > 2 > 461-477

Journal of Computational and Applied Mathematics > 2007 > 202 > 1 > 105-121

Journal of Computational and Applied Mathematics > 2007 > 204 > 2 > 356-362

Journal of Computational and Applied Mathematics > 2007 > 206 > 1 > 454-472