Characteristic functions and -orthogonality properties of Chebyshev polynomials of third and fourth kind.
Characterization theorem's of Hermite polynomials.
Characterizations of classical polynomials
Chebyshev polynomials and some methods of approximation.
Circular digraph walks, -balanced strings, lattice paths and Chebychev polynomials.
Classical 2-orthogonal polynomials and differential equations.
Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials
In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.
Classical orthogonal polynomials and Leverrier-Faddeev algorithm for the matrix pencils .
Classical Polynomials - A Unified Presentation
Classical polynomials - a unified presentation.
Closed-form expression for Hankel determinants of the Narayana polynomials
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana...
Coda to a theorem of Schur.
Combinatorial interpretations of the Jacobi-Stirling numbers.
Combinatorics of identities involving Meixner polynomials. (Combinatoire des identités sur les polynômes de Meixner.)
Commuting polynomial vectors over an integral domain
Complete Systems of Hermite Associated Functions
It is proved that if the increasing sequence kn n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of CRthen the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.
Complex and distributional weights for sieved ultraspherical polynomials.
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Connections between Romanovski and other polynomials
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.
Consistency of trigonometric and polynomial regression estimators
The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials , k=0,1,..., for the observation model , i=1,...,n, where the are independent random variables with zero mean value and finite variance, and the observation points , i=1,...,n, form a random sample from a distribution with density . Sufficient and necessary conditions are obtained for consistency in the sense of the errors , ,...