On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On zeros of regular orthogonal polynomials on the unit circle
A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.
One-parameter system of functional equation. (Summary).
Opérateurs hypergéométriques réductibles : décompositions et groupes de Galois différentiels
Operational identities for circular and hyperbolic functions and their generalizations.
Operational properties of a generalized Hermite transformation.
Operational relations related to a function defined by a generalized Rodrigues' formula.
Operator representation of fermi-Dirac and Bose-Einstein integral functions with applications.
Operator representations of generalized hypergeometric functions and certain polynomials
Operatormethoden für q-Identitäten II: q-Laguerre Polynome.
Operators preserving orthogonality of polynomials
Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions for polynomials...
Operator-valued Bessel functions on Jordan algebras.
Optimization of parameters in the Menzerath–Altmann law
Four formulas of the Menzerath–Altmann law are tested from the point of view of their applicability and suitability. The accuracy of related approximations of measured data is examined by the least square method at first. Then the accuracy of calculated parameters in the formulas under consideration is compared statistically. The influence of neglecting parameter is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics....
Optimization of Rational Approximations by Continued Fractions
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x), an upper bound ε(f) of the relative error is needed, where ε(f) itself depends on the error bounds ε(app); ε(eval) of the approximation and evaluation error respectively. The approximation function g(x) ≈ f(x) is a rational function (Remez algorithm), and with sufficiently high polynomial degrees ε(app) becomes...
Orbit functions.
Orthoexponential polynomials and the Legendre polynomials
Orthoexponential polynomials can be expressed in terms of the Legendre polynomials. The formulae proved in this paper are useful for the computation of the values of orthoexponential polynomials. It is also possible to re-state, for orthoexponential polynomials, some theorems from the theory of classical orthogonal polynomials.
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line.
Orthogonal least squares solutions for linear operators.
Orthogonal polynomial ensembles in probability theory.
Orthogonal polynomials.