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 …

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 …

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 …

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 …

Bessel’s equation is a second-order differential equation with two linearly independent solutions. A second-order differential equation has two independent variables, where the highest order derivative …

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 …

(2.2) These solutions are called Bessel functions of the first kind of order ±v.

Friedrich Wilhelm Bessel (German: [ˈbɛsl̩]; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values …

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 …