What are Bessel functions

Bessel functions

• J0, J1, Jn, Y0, Y1, Yn - Bessel functions of the first and second kind

• I0, I1, In, K0, K1, Kn - Changed (hyperbolic) Bessel functions

• H1, H2 - Hankel functions

• Ai, DAi, Bi, DBi - Airy functions

• bei, ber - Bessel-Kelvin functions

• js, ys - spherical Bessel functions


• Fractions and negative orders are supported for most Bessel functions.

• If the arguments of the Bessel function take on very large positive or negative values, this can lead to overflow or underflow errors. If your calculations require these values, you may be able to use the scaled versions of the functions instead.

• The scaled version of a Bessel function is formed by entering .sc after the function name to get Ai.sc, or by entering sc as a subscript to get Aisc. The scale expression for the scaled version is shown with the description of each function.

• In the mathematical literature, Bessel functions such as J0 (z) are sometimes referred to as indexed functions. PTC Mathcad does not use subscripts to represent such functions. For example, J0 (z) is represented by PTC Mathcad as J0 (z).

Related topics

Special functions

Functions that can be evaluated numerically as well as symbolically

Example: Bessel functions