A Bochner theorem for Dunkl polynomials.
A characterization of the orthogonal polynomials.
A matrix analysis of the stability of the Clenshaw algorithm.
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
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.
Continuous symmetrized Sobolev inner products of order . II.
Determinant inequalities for sieved ultraspherical polynomials.
Die Interpolation durch Bernoulli'sche Funktionen
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle.
Generalized coherent states for oscillators connected with Meixner and Meixner-Pollaczek polynomials.
Jacobi-Sobolev orthogonal polynomials: asymptotics for -coherence of measures.
Leonard pairs from the equitable basis of .
New quadrature rules for Bernstein measures on the interval .
On a class of integrals involving a Bessel function times Gegenbauer polynomials.
On certain Heun functions, associated functions of discrete variables, and applications.
On hypergeometric functions and Pochhammer -symbol.
On pseudo Hermite matrix polynomials of two variables.
On the Krall-type polynomials.
Orthogonal least squares solutions for linear operators.
Orthogonal polynomials.