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Weber's Discontinuous Integrals


 int_0^inftyJ_0(ax)cos(cx)dx={0   a<c; 1/(sqrt(a^2-c^2))   a>c
(1)
 int_0^inftyJ_0(ax)sin(cx)dx={1/(sqrt(c^2-a^2))   a<c; 0   a>c,
(2)

where J_0(z) is a zeroth order Bessel function of the first kind.


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References

Bowman, F. Introduction to Bessel Functions. New York: Dover, pp. 59-60, 1958.

Referenced on Wolfram|Alpha

Weber's Discontinuous Integrals

Cite this as:

Weisstein, Eric W. "Weber's Discontinuous Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WebersDiscontinuousIntegrals.html

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