Airy-Fock Functions

The three Airy-Fock functions are

$$\nu(z) = {\textstyle{1\over 2}}\sqrt{\pi}\mathop{\rm Ai}\nolimits (z)$$ (1)

$$w_1(z) = 2e^{i\pi/6}\nu(\omega z)$$ (2)

$$w_2(z) = 2e^{-i\pi/6}\nu(\omega^{-1}z),$$ (3)

where $\mathop{\rm Ai}\nolimits (z)$ is an Airy Function. These functions satisfy

$$\nu(z)={w_1(z)-w_2(z)\over 2i}$$ (4)

$$[w_1(z)]^*=w_2(z^*),$$ (5)

where $z^*$ is the Complex Conjugate of $z$.

See also Airy Functions

References

Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ``Mathematical Encyclopaedia.'' Dordrecht, Netherlands: Reidel, p. 65, 1988.