z
2 y
00
þ zy
0
À z
2
þ n
2
À
Á
y ¼ 0
ðD:3Þ
Modified Bessel functions of the first kind, I n (z), are used in NRVS theory to
calculate the fractional contribution of different transitions to the normalized excitation probability (see [481]). In Mathematica they are defined by BesselI[n,z]
(Fig. D.3).
Modified Bessel functions of the second kind, K n (z), are needed to describe the
spectral properties of bend magnets. In Mathematica they are defined by BesselK[n,
z]. Like the regular Bessel functions of the second kind, they have a singularity as
z ! 0 (Fig. D.4).
Fig. D.3 Modified Bessel
functions of the first kind
Fig. D.4 Modified Bessel function of the second kind
Appendix D: Special Functions for Synchrotron Radiation
321
2 y
00
þ zy
0
À z
2
þ n
2
À
Á
y ¼ 0
ðD:3Þ
Modified Bessel functions of the first kind, I n (z), are used in NRVS theory to
calculate the fractional contribution of different transitions to the normalized excitation probability (see [481]). In Mathematica they are defined by BesselI[n,z]
(Fig. D.3).
Modified Bessel functions of the second kind, K n (z), are needed to describe the
spectral properties of bend magnets. In Mathematica they are defined by BesselK[n,
z]. Like the regular Bessel functions of the second kind, they have a singularity as
z ! 0 (Fig. D.4).
Fig. D.3 Modified Bessel
functions of the first kind
Fig. D.4 Modified Bessel function of the second kind
Appendix D: Special Functions for Synchrotron Radiation
321