# Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 239-253

_{x}

_{x}+ 2Bu

_{x}

_{y}+ Cu

_{y}

_{y}+ Du

_{x}+ Eu

_{y}= λ

_{n}u has orthogonal polynomial solutions, then the differential operator L[.] must be symmetrizable and can not be parabolic in any nonempty open subset of the plane. We also find Rodrigues type formula for orthogonal polynomial...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 287-297

_{n})

_{n}

_{N}

_{0}on the nonnegative integers arising from isotropic random walks on distance transitive graphs. The laws of those isotropic random walks converge in distribution to the normal distribution and the transition probabilities of the S

_{n}are closely related with a sequence of Bernstein-Szego polynomials. We give an explicit...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 311-318

_{n}}

^{~}

_{n}

_{=}

_{-}

_{~}be a doubly infinite sequence of real numbers. A solution of the strong Hamburger moment problem is a positive measure σ on (-~, ~) such that c

_{n}= ∫

^{~}

_{-}

_{~}u

^{n}dσ(u) for n = 0, +/- 1, +/- 2,.... A solution of the strong Stieltjes moment problem is a positive measure σ on [0, ~) such that c

_{n}= ∫

^{~}...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 3-14

_{n}) of orthogonal polynomials on the unit circle from a new point of view. Whenever the polynomials Φ ...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 167-175

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 195-203

^{p}

_{v}[a, b] be the class of continuous functions in the interval [a, b], which admit analytic continuation to H

^{p}in the subintervals of a v-subdivition of [a, b]. Let S

_{n}

_{,}

_{v}[a, b] be the set of piecewise rational functions which have pieces of degree n and no more than v breakpoints. The paper deals with the construction of f

_{n}

_{,}...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 189-194

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 373-385

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 119-128

_{n}[f] = ∫

_{R}w(x) f

^{(}

^{n}

^{)}(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 205-217

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 529-533

^{(}

^{α}

^{)}

_{n}(x), α R is given.

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 275-286

^{2}

^{s}(i.e., the q-analogues of Charlier, Meixner, Krawtchouk and Hahn polynomials), in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function , and the...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 255-274

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 327-335

_{ω}

_{-}>

_{0}P

_{n}(x(s, ω)) = Q

_{n}(s), where P

_{n}(s) and Q

_{n}(s) stand for the...

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 91-103

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 37-45

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

Journal of Computational and Applied Mathematics > 1998 > 99 > 1-2 > 143-154

_{n}, γ

_{n}of orthogonal polynomials with respect to a D

_{ω}semi-classical linear form are derived. D

_{ω}is the difference operator. The limit when ω -> 0 are also investigated recovering known results. Applications to generalized Meixner polynomials of class one are also treated.