Error Estimates in simple quadrature with Voigt functions

Error Estimates for Gauss Quadrature Formulas for Analytic Functions

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

Quadrature Error Estimates Involving Moduli of Continuity of Derivatives

Evaluation of the Asymmetric Voigt Profile and Complex Error Functions in Terms of the Kummer Functions

In this work we present the explicit representations of the Voigt function K(a, b) (the convolution between a Gaussian and a Lorentzian function), the function N(a, b) defined as the convolution of Gaussian and dispersion distributions as well as the complex error function erf(a + ib), all in terms of the Kummer functions M(α, γ, a). The expansions are valid for all values of the parameter a (t...

Asymptotic Error Estimates for the Gauss Quadrature Formula

New Error Coefficients for Estimating Quadrature Errors for Analytic Functions

Since properly normalized Chebyshev polynomials of the first kind T„(z) satisfy (?„, ?„) = [ f,(z)7ÜÖ |1 z2\~TM\dz\ = Smn for ellipses ep with foci at ± 1, any function analytic in ep has an expansion,/(z) = J3 anfn{z) with a„ = (/, Tn). Applying the integration error operator E yields E(J) = 2~Z a„E(Tn)Applying the Cauchy-Schwarz inequality to E(J) leads to the inequality |£CDIsá Z W¿2\E(Tn)\2...