Airy Bi

and $\mathrm{Bi}$ (sometimes called the "Bairy function") are linearly independent solutions of the Airy differential equation $$y(z)-zy(z)=0.$$

• Airyai.png

  Airy $\mathrm{Ai}$ function.

• Airybi.png

  Aairy $\mathrm{Bi}$ function.

• Complexairyai.png

  Domain coloring of analytic continuation of $\mathrm{Ai}$.

• Complexairybi.png

  Domain coloring of analytic continuation of $\mathrm{Bi}$.

Videos

Airy differential equation
Series solution of ode: Airy's equation
Leading Tsunami wave reaching the shore

References

The mathematics of rainbows
Tables of Weyl Fractional Integrals for the Airy Function
Special Functions: An Introduction to the Classical Functions of Mathematical Physics
Airy function zeros