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Supersymmetric Partner Bessel Functions

The partner Bessel functions are given by . The supersymmetry (SUSY) parameter determines the transition beween Bessel functions of different order, from to for arbitrary .

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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.
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