Highly Accurate, Numerical Method for Calculating Mathematical Functions Defined by Integrals: Feedback from Numerical Analysis for Quantum Mechanics to Mathematics and Numerical Analysis

摘要

We applied a method for calculating indefinite integrals developed for atomic structure calculations to mathematical functions defined by integrals and obtained highly accurate results. The method is simple and has wide applicability. Examples of application are, elementary transcendental functions such as exponential, logarithmic, and arctangent functions, then error function, Fresnel integrals, exponential, cosine, and sine integrals, and incomplete gamma functions.