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, 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 solutions of one …

Dec 3, 2025 · The Bessel functions of the first kind are defined as the solutions to the Bessel differential equation

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. Consequently, we here …

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.

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 formulas …

May 24, 2024 · The radial equation leads to a Bessel equation. The Bessel function solutions describe the radial part of the solution and one does not expect a singular solution at the center of the drum. …

Apr 4, 2025 · Named after the German mathematician Friedrich Bessel, these functions are fundamental in solving a class of differential equations that arise naturally in systems with cylindrical or spherical …

BESSEL EQUATIONS AND BESSEL FUNCTIONS Bessel functions form a cla. s of the so called special functions. They are im-portant in math as well as in physic. l sciences (physics and …