Synchrotron function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> the synchrotron functions are defined as follows (for x ≥ 0):

<ul><li>First synchrotron function 
 
 
 
 F
 (
 x
 )
 =
 x
 
 ∫
 
 x
 
 
 ∞
 
 
 
 K
 
 
 5
 3
 
 
 
 (
 t
 )
 
 d
 t
 
 
 {\displaystyle F(x)=x\int _{x}^{\infty }K_{\frac {5}{3}}(t)\,dt}
 
</li>
<li>Second synchrotron function 
 
 
 
 G
 (
 x
 )
 =
 x
 
 K
 
 
 2
 3
 
 
 
 (
 x
 )
 
 
 {\displaystyle G(x)=xK_{\frac {2}{3}}(x)}
 
</li></ul>
where Kj is the modified <a href="/facts/Bessel_function/hSyvFPqC">Bessel function</a> of the second kind.

Synchrotron function open-in-new

Synchrotron function