Quadrature formulas and taylor series of secant and tangent

Abstract

Second-order quadrature formulas and their fourth-order expansions are derived from the Taylor series of the secant and tangent functions. The errors of the approximations are compared to the error of the midpoint approximation. Third and fourth order quadrature formulas are constructed as linear combinations of the second-order approximations and the trapezoidal approximation

Keywords

• Quadrature formula
• Fourier transform
• generating function
• Euler-Mclaurin formula