Synchrotron function


In mathematics the synchrotron functions are defined as follows :
where Kj is the modified Bessel function of the second kind.

Use in Astrophysics

In astrophysics, x is usually a ratio of frequencies, that is, the frequency over a critical frequency. This is needed when calculating the spectra for different types of synchrotron emission. It takes a spectrum of electrons generated by a separate process and converts this to the spectrum of photons generated by the input electrons/positrons.
For further information, see High Energy Astrophysics, Malcolm S. Longair, CUP, 1990.