Examples for

Bessel & Related Functions

Bessel functions are defined as solutions of a second-order differential equation, namely Bessel's differential equation. Commonly, there are two classes of solutions, called Bessel functions of the first kind and Bessel functions of the second kind. The linear combinations of these two are usually called Bessel functions of the third kind, or Hankel functions. Wolfram|Alpha has the ability to compute properties for the family of Bessel functions, as well as other Bessel-related functions, such as Airy and Struve functions.

Bessel Functions

Compute properties for different kinds of Bessel functions.

Plot a Bessel function of the first kind:

Integrate a spherical Bessel function:

Find differential equations satisfied by a Bessel function of the second kind:

Struve Functions

Compute properties for the Struve H function and modified Struve L function.

Find information about the Struve functions:

Airy Functions

Compute properties for four varieties of Airy functions.

Compute a value of an Airy function to high precision:

Plot an Airy function:

Find relations between functions:

Find differential equations satisfied by an Airy function:

Hankel Functions

Compute properties for Hankel functions of the first and the second kind.

Generate information about the Hankel functions:

Compute information about the spherical Hankel functions: