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 …

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 …

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. …

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, …

Bessel, a German astronomer, was born in Minden, Prussia, in 1784 and died in K ̈onigsberg, Prussia (now Russia) in 1846. At the age of 20, he recalculated the orbit of Halley’s comet, …

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 …

Dec 22, 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 …

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 $\nu = 1$ …

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 …

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 …