Synchrotron function: Difference between revisions

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In [[mathematics]] the '''synchrotron functions''' are defined as follows (for ''x'' &ge; 0):<ref>{{Cite journal |last1=Fouka |first1=M. |last2=Ouichaoui |first2=S. |date=2013-01-29 |title=Analytical Fits to the Synchrotron Functions |journal=Research in Astronomy and Astrophysics |volume=13 |issue=6 |pages=680–686 |language=en |doi=10.1088/1674-4527/13/6/007|arxiv=1301.6908 |bibcode=2013RAA....13..680F |s2cid=118480582 }}</ref>

* First synchrotron function <math display="block">F(x) = x \int_x^\infty K_{\frac{5}{3}}(t)\,dt</math>

:* Second synchrotron function <math display="block">G(x) = x K_{\frac{2}{3}}(x)</math>

:<math>F(x) = x \int_x^\infty K_{\frac{5}{3}}(t)\,dt</math>

* Second synchrotron function

:<math>G(x) = x K_{\frac{2}{3}}(x)</math>

where ''K''_''j'' is the modified [[Bessel function]] of the second kind.