Watson-Nicholson Formula

Let be a Hankel function of the first or second kind, let , and define

Then

$H_nu^((iota))(x)=3^(-1/2)wexp{(-1)^(iota+1)i[pi/6+nu(w-1/3w^3 -tan^(-1)w)]}H_(1/3)^((iota))(1/3nuw)+O|nu^(-1)|.$

See also

Hankel Function of the First Kind, Hankel Function of the Second Kind, Watson's Formula

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References

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

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Watson-Nicholson Formula

Cite this as:

Weisstein, Eric W. "Watson-Nicholson Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Watson-NicholsonFormula.html

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