A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi‐infinite integrals

With the advent of computers and scientific computing, there has been a push to develop more accurate and more efficient techniques in computing challenging problems in applied mathematics. In the numerical evaluation of semi‐infinite integrals, a common problem in applied mathematics, three general methods have come to the forefront. To wit, these general methods are known as extrapolation methods, sequence transformations and steepest descent methods. In this work, we put these three general methods to the test on three prototypical semi‐infinite integrals exhibiting oscillatory and exponential properties. On the bases of accuracy and efficiency, we compare and contrast the three general methods for computing infinite‐range integrals. Through the numerical examples, we introduced refinements improving the accuracy and efficiency of the algorithms obtained from the three aforementioned methods.