Supersymmetric Partner Bessel Functions

The partner Bessel equation

is derived from a supersymmetric (SUSY) type of factorization of Bessel's equation, which also applies to other Sturm–Liouville equations. The partner Bessel functions show an interesting and unusual SUSY behavior: the SUSY parameter γ links these functions to a pair of Bessel functions differing by two orders

.

Since , this SUSY parameter takes the partner Bessel functions from to .

In the snapshots you can see the shape of the partner Bessel functions as they evolve from one order to another for different values of the SUSY parameter.

References:

[1] N. Barbosa-Cendejas and M. A. Reyes, "Damped Wave Equation from Isospectral Bessel Functions," Rev. Mex. Fís., 54, 2008 pp. 319–321.
[2] M. A. Reyes, D. Jimenez, and H. C. Rosu, "One-Parameter Isospectral Special Functions," Rev. Mex. Fís., 49, 2003 pp. 358–363.