Bessel functions are defined as linear independent solutions of equation

This equation often arises when solving Laplas and Helmholtz equations in spherical or cylindric coordinates (electromagnetic wave transmission, transmission of heat and diffusion).

Bessel functions of the first kind, denoted as *J _{α }(x)*, are solutions of Bessel's differential equation that are finite at the origin (

Subroutines in this module calculate the values of Bessel functions of integer order. Bessel functions of fractional order could be calculated by using the subroutines from another module.

**BesselJ0**, **BesselJ1** and **BesselJN** subroutines calculate the Bessel functions of the first kind of 0th, 1st and N-th order. **BesselY0**, **BesselY1** and **BesselYN** subroutines calculate the Bessel functions of the second kind of 0th, 1st and N-th order. **BesselI0** and **BesselI1** subroutines calculate the modified Bessel functions of the first kind of 0th and 1st order. **BesselK0**, **BesselK1** and **BesselKN** subroutines calculate the modified Bessel functions of the second kind of 0th, 1st and N-th order.

Piecewise rational approximation and Chebyshev polynomial approximation are used to calculate functions of 0th and 1st order, forward and backward recurrence and series expansion are used for higher order functions.

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