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

4 days ago · The Bessel functions of the first kind are defined as the solutions to the Bessel differential equation

The function w(z; t) is called the generating function of the Bessel functions of integer order, and formula (B.26) plays an important role in the theory of these functions.

Oct 7, 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 …

Bessel functions and closely related functions form a rich area of mathe-matical analysis with many representations, many interesting and useful prop-erties, and many interrelations.

This chapter is based in part on Abramowitz and Stegun (1964, Chapters 9, 10, and 11) by F. W. J. Olver, H. A. Antosiewicz, and Y. L. Luke, respectively.

We start our detailed study of Bessel functions by introducing a generating function yield-ing the Jn for integer n (of either sign).

May 24, 2024 · Bessel functions satisfy a variety of properties, which we will only list at this time for Bessel functions of the first kind. The reader will have the opportunity to prove these for …

The Bessel function of the third kind, also called a Hankel function or Weber function is a complex-valued solution to Bessel’s differential equation. Essentially, the Bessel function of …

Apr 4, 2025 · This article introduces the key types of Bessel functions, explains the governing equations and relationships, and highlights their wide-ranging applications across engineering, …