On Appel-type quadrature rules.
On calculation of zeta function of integral matrix
Values of the Epstein zeta function of a positive definite matrix and the knowledge of matrices with minimal values of the Epstein zeta function are important in various mathematical disciplines. Analytic expressions for the matrix theta functions of integral matrices can be used for evaluation of the Epstein zeta function of matrices. As an example, principal coefficients in asymptotic expansions of variance of the lattice point count in the random ball are calculated for some lattices.
On convergence and divergence of Fourier-Bessel series.
On the modes of polynomials derived from nondecreasing sequences.
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...
Orthogonality of Jacobi polynomials with general parameters.