Weber's Discontinuous Integrals

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

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

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

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Weber's Discontinuous Integrals

Cite this as:

Weisstein, Eric W. "Weber's Discontinuous Integrals." From MathWorld--A Wolfram Web Resource.

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