Modified Bessel K

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.

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  Graph of $K_0$.

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  Graphs of $K_0$, $K_1$, $K_2$, and $K_3$.

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  Domain coloring of $K_1$.

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  Modified Bessel functions from Abramowitz&Stegun.

Properties

Relationship between Airy Ai and modified Bessel K

References

[1]

Bessel functions

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Anger function

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Bessel-Clifford

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Bessel $J_{\nu}$

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Bessel $Y_{\nu}$

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Bessel $I_{\nu}$

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Modified Bessel $K_{\nu}$

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Spherical Bessel $j_{\nu}$

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Spherical Bessel $y_{\nu}$