Modified Bessel I

The modified Bessel function of the first kind is defined by $$I_{\nu}(z)=i^{-\nu}J_{\nu}(iz),$$ where $i$ denotes the imaginary number and $J_{\nu}$ denotes the Bessel function of the first kind.

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  Graph of $I_0$.

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  Graph of $I_1$.

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  Graph of $I_0$,$I_1$,$I_2$, and $I_3$.

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  Domain coloring of $I_0$.

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  Domain coloring of $I_0$.

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  Modified Bessel functions from Abramowitz&Stegun.

Properties

Relationship between Bessel I sub -1/2 and cosh
Relationship between Bessel I sub 1/2 and sinh
Relationship between Bessel I sub n and Bessel J sub n
Relationship between Airy Bi and modified Bessel I

References

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 $y_{\nu}$