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Weyrich's Formula

Weyrich's formula states that for r and x real, with 0<=arg(sqrt(k^2-tau^2))<pi and 0<=argk<pi,

1/2iint_(-infty)^inftyH_0^((1))(rsqrt(k^2-tau^2))e^(itaux)dtau=(e^(iksqrt(r^2+x^2)))/(sqrt(r^2+x^2)),

where H_0^((1))(z) is a Hankel function of the first kind.

See also

Hankel Function of the First Kind

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References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.

Referenced on Wolfram|Alpha

Weyrich's Formula

Cite this as:

Weisstein, Eric W. "Weyrich's Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WeyrichsFormula.html

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