# Modified Bessel I

From specialfunctionswiki

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.

Domain coloring of $I_0$.

Domain coloring of $I_0$.

# 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**