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, …

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Feb 7, 2026 · 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 …

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3 days ago · 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 …

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, …

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. …