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 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.

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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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