Bessel function - Wikipedia
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 conduction, …
Bessel function | Definition, Equation, Uses, & Facts | Britannica
Dec 26, 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 …
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 Function -- from Wolfram MathWorld
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 and Bessel …
Bessel functions explained - Product Development Engineers Ltd
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 …
BesselFunctions - Wichita State University
This value will be referred to as the order of the equation and the solutions are called Bessel functions of order $\nu$. We will look at 3 cases, $\nu = 0$, $\nu = \frac {1} {2}$, and $\nu = 1$ and the solutions …
DLMF: Chapter 10 Bessel Functions - NIST
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, 10, …
Bessel functions - Encyclopedia of Mathematics
Jul 18, 2025 · If the order is even, the Bessel function is even, if odd, it is odd. If $\nu$ is real and the argument is real, it is a common convention to take the determination of $z^\nu$ which takes real …
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 …
4.6: Bessel Functions - Mathematics LibreTexts
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, describing …