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 …

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. …

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 …

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 …

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 …

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 $\nu = 1$ …

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 …

May 24, 2024 · The r 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 …

Solutions to (1) are known as Bessel functions. Since (1) is a second order homogeneous linear equation, the general solution is a linear combination of any two linearly independent (i.e. …

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 …