Difference between revisions of "Modified Bessel K"

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=Properties=
 
=Properties=
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<strong>Proposition:</strong> The following formula holds:
 
$$K_{\frac{1}{2}}(z)=\sqrt{\dfrac{\pi}{2}}\dfrac{e^{-z}}{\sqrt{z}}; z>0.$$
 
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<strong>Proof:</strong> █
 
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[[Relationship between Airy Ai and modified Bessel K]]
 
[[Relationship between Airy Ai and modified Bessel K]]
 
<center>{{:Bessel functions footer}}</center>
 
  
 
=References=
 
=References=
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[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]
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{{:Bessel functions footer}}

Revision as of 19:15, 10 June 2016

The modified Bessel function of the second kind is defined by $$K_{\nu}(z)=\dfrac{\pi}{2} \dfrac{I_{-\nu}(z)-I_{\nu}(z)}{\sin(\nu \pi)},$$ where $I_{\nu}$ is the modified Bessel function of the first kind.


Properties

Relationship between Airy Ai and modified Bessel K

References

[1]

Bessel functions