Bessel functions describe the radial part of vibrations of a circular membrane. Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat …

Nov 18, 2025 · Bessel function, any of a set of mathematical functions systematically derived around 1817 by the German astronomer Friedrich Wilhelm Bessel during an investigation of …

As Rainville pointed out in his classic booklet [Rainville (1960)], no other special functions have received such detailed treatment in readily available treatises as the Bessel functions. …

Like sines and cosines, Bessel functions are solutions of a differential equation; they are tabulated and their graphs can be drawn; they can be represented as a series; and a large number of …

Dec 3, 2025 · The Bessel functions are more frequently defined as solutions to the differential equation. There are two main classes of solution, called the Bessel function of the first kind …

It was the first major treatise on Bessel functions in English and covered topics such as applications of Bessel functions to electricity, hydrodynamics and diffraction.

Maximon Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, D.C. This chapter is based in part on Abramowitz and Stegun (1964, Chapters 9, …

May 24, 2024 · The history of Bessel functions, did not just originate in the study of the wave and heat equations. These solutions originally came up in the study of the Kepler problem, …

Oct 29, 2008 · This paper derives the Bessel functions through use of a series solution to a di erential equation, develops the di erent kinds of Bessel functions, and explores the topic of …

Approximation (24) permits also to approximate the positive zeros of Bessel functions, that is solutions of J (x) = 0. All except possibly one of them are close to the zeros of cos(z =2 =4).