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Airy-Fock Functions

The three Airy-Fock functions are

$\displaystyle \nu(z)$ $\textstyle =$ $\displaystyle {\textstyle{1\over 2}}\sqrt{\pi}\mathop{\rm Ai}\nolimits (z)$ (1)
$\displaystyle w_1(z)$ $\textstyle =$ $\displaystyle 2e^{i\pi/6}\nu(\omega z)$ (2)
$\displaystyle w_2(z)$ $\textstyle =$ $\displaystyle 2e^{-i\pi/6}\nu(\omega^{-1}z),$ (3)

where $\mathop{\rm Ai}\nolimits (z)$ is an Airy Function. These functions satisfy
\nu(z)={w_1(z)-w_2(z)\over 2i}
\end{displaymath} (4)

\end{displaymath} (5)

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

See also Airy Functions


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

© 1996-9 Eric W. Weisstein