Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration

Error estimates with explicit constants are given for approximations of functions, definite integrals and indefinite integrals by means of the Sinc approximation. Although in the literature various estimates have already been given for these approximations, they were basically for examining the rates of convergence, and several constants were left unevaluated. Giving more explicit estimates, i.e., evaluating these constants is of great practical importance, since by which we can reinforce the useful formulas with the concept of “verified numerical computations.” We also improve some formulas themselves to decrease their computational costs. Numerical examples that confirm the theory are also given.