A mixed quadrature rule of modified Birkhoff-Young rule and $SM_2(f)$ rule for the numerical integration of analytic functions

Abstract

A quadrature rule of higher precision is constructed in this paper by mixing two quadrature rules of lower precision for an approximate evaluation of the integral of an analytic function over a line segment in the complex plane. An asymptotic error estimate of the rule is also determined and the rule is numerically verified.