Difference between revisions of "Modified Bessel K"
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Revision as of 09:26, 5 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.
Domain coloring of $K_1(z)$.
Modified Bessel functions from Abramowitz&Stegun.
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Properties
Proposition: The following formula holds: $$K_{\frac{1}{2}}(z)=\sqrt{\dfrac{\pi}{2}}\dfrac{e^{-z}}{\sqrt{z}}; z>0.$$
Proof: █
Relationship between Airy Ai and modified Bessel K
Modified Bessel $K_{\nu}$
