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Lipschitz's Integral


\begin{displaymath}
\int_0^\infty e^{-ax} J_0(bx)\,dx = {1\over\sqrt{a^2+b^2}},
\end{displaymath}

where $J_0(z)$ is the zeroth order Bessel Function of the First Kind.


References

Bowman, F. Introduction to Bessel Functions. New York: Dover, p. 58, 1958.




© 1996-9 Eric W. Weisstein
1999-05-25