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, …

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. …

Oct 7, 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 …

4 days ago · The Bessel functions of the first kind are defined as the solutions to the Bessel differential equation

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, …

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 …

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, …

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 $\nu = 1$ …

Jul 18, 2025 · In this entry the term is used for the cylinder functions of the first kind (which are usually called Bessel functions of the first kind by those authors which use the term Bessel …

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 …