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 (x = 0) for non-negative integer α, and diverge as x approaches zero for negative non-integer α. α is referred to as the order of the Bessel function. Bessel function of the second kind is the second solution of Bessel's differential equation (the solutions are linear independent). Bessel functions could be extended on a complex plane. The important special case are modified Bessel functions I_α (x) and K_α (x) - linear combinations of pure imaginary arguments which possess real values.

Subroutines from this module calculate fractional order Bessel functions. BesselJV subroutine calculates the value of the function of the first kind, BesselIV calculates the value of the modified function of the first kind. Values of functions of the second kind for non-integer orders could be calculated by using the following formulas:

If the function order is integer, the above formulas could not be used, but in this case you can use the subroutines calculating the values of Bessel functions of integer orders.

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C#

C# 1.0 source.
besselv.csharp.zip - Bessel functions of fractional order

C++

C++ source.
besselv.cpp.zip - Bessel functions of fractional order
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
besselv.delphi.zip - Bessel functions of fractional order

Visual Basic 6

Visual Basic 6 source.
besselv.vb6.zip - Bessel functions of fractional order

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
besselv.zonnon.zip - Bessel functions of fractional order