TOPICS
Search

Weyrich's Formula

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

Explore with Wolfram|Alpha

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 Web Resource. https://mathworld.wolfram.com/WeyrichsFormula.html

Subject classifications