info prev up next book cdrom email home

Watson-Nicholson Formula

Let $H_\nu^{(\iota)}(x)$ be a Hankel Function of the First or Second Kind, let $x, \nu>0$, and define

\begin{displaymath}
w=\sqrt{\left({x\over\nu}\right)^2-1}.
\end{displaymath}

Then


\begin{displaymath}
H_\nu^{(\iota)}(x)=3^{-1/2}w\mathop{\rm exp}\nolimits \{(-1)...
...}({\textstyle{1\over 3}}\nu w)+{\mathcal O}\vert\nu^{-1}\vert.
\end{displaymath}


References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1475, 1980.




© 1996-9 Eric W. Weisstein
1999-05-26