Bessel functions of the second kind, Y n (z), are needed to describe the properties of
undulators, and in Mathematica they are defined by BesselY[n,z]. As seen in
Fig. D.2, they have a singularity at the origin (Fig. D.2).
Appendix D.2:Modified Bessel Functions
As with regular Bessel functions, there are two modified Bessel functions, I n (z) and
K n (z). They are independent solutions to the differential equation:
Fig. D.1 Bessel functions of the first kind
Fig. D.2 Bessel functions of the second kind
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Appendix D: Special Functions for Synchrotron Radiation