The Watson-Nicholson formula gives an asymptotic expression for Hankel functions. Let 
be a Hankel
function of the first or second
kind, let 
,
and define
 |
Then
![H_nu^((iota))(x)=3^(-1/2)wexp{(-1)^(iota+1)i[pi/6+nu(w-1/3w^3
-tan^(-1)w)]}H_(1/3)^((iota))(1/3nuw)+O|nu^(-1)|.](/images/equations/Watson-NicholsonFormula/NumberedEquation2.svg) |
Watson-Nicholson Formula
See also
Hankel Function of the First Kind, Hankel Function of the Second Kind, Watson's FormulaExplore with Wolfram|Alpha
References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1475, 1980.Referenced on Wolfram|Alpha
Watson-Nicholson FormulaCite this as:
Weisstein, Eric W. "Watson-Nicholson Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Watson-NicholsonFormula.html