Mr. Bessel’s eponymous functions

This article discusses the use of Bessel functions, specifically J1, in evaluating a definite integral via the trapezoid rule. It explains how the integral can be expressed in terms of a Bessel function using a change of variables and the integral definition of Bessel functions. The post also explores the historical context of Bessel functions, their definitions (power series, differential equations, integral representation), and their origin in celestial mechanics. It highlights the utility of Bessel functions as well-studied tools for computation, even in simple calculators like bc. The content is mathematical and technical, focusing on applied mathematics and numerical methods relevant to IT and technology.