Sharp bounds on the mathematical constant e.
Simple Monte Carlo integration with respect to Bernoulli convolutions
We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit...
Some double integral inequalities and applications.
Some Gauss-Type Formulae for the Evaluation of Cauchy Principal Values of Integrals.
Some generalized error inequalities and applications.
Some methods of numerical integration over a semi-infinite interval
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Studies on the differential equations of enzyme kinetics. II: Bimolecular reaction: The fitting of experimental data to the simplified model.
Sur les quadratures.