Bessel Function in Python SciPy - Search localsearch

wikipedia.org

https://en.wikipedia.org/wiki/Bessel_function

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 conduction, and other physical phenomena with circular symmetry or cylindrical symmetry.

britannica.com

https://www.britannica.com/science/Bessel-function

Bessel function | Definition, Equation, Uses, & Facts | Britannica

Bessel function, any of a set of mathematical functions systematically derived around 1817 by the German astronomer Friedrich Wilhelm Bessel. They arise in the solution of Laplace’s equation when the latter is formulated in cylindrical coordinates. Learn more about Bessel functions in this article.

brown.edu

https://appliedmath.brown.edu/sites/default/files/…

The Bessel Functions - Brown University

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 present only a brief introduction to the subject including the related Laplace transform pairs used in this book.

udel.edu

https://www.physics.udel.edu/~jim/PHYS607_18S/Clas…

USEFUL FACTS AND FORMULAS FOR BESSEL FUNCTIONS 2. Bessel functions of ...

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

nist.gov

https://dlmf.nist.gov/10

DLMF: Chapter 10 Bessel Functions - NIST

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, and 11) by F. W. J. Olver, H. A. Antosiewicz, and Y. L. Luke, respectively.

product-development-engineers.com

https://product-development-engineers.com/2025/04/…

Bessel functions explained - Product Development Engineers Ltd

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 symmetry.

encyclopediaofmath.org

https://encyclopediaofmath.org/wiki/Bessel_functio…

Bessel functions - Encyclopedia of Mathematics

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 functions for all cylinder functions).

wolfram.com

https://mathworld.wolfram.com/BesselFunction.html

Bessel Function -- from Wolfram MathWorld

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 function of the second kind .

statisticshowto.com

https://www.statisticshowto.com/differential-equat…

Bessel Function: Simple Definition, Characteristics - Statistics How To

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 is the second derivative.

byu.edu

https://physics.byu.edu/faculty/colton/docs/phy471…

Bessel Functions - physics.byu.edu

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 about them are known.”