info prev up next book cdrom email home

Weber's Discontinuous Integrals


\begin{displaymath}
\int_0^\infty J_0(ax)\cos (cx)\,dx =\cases{
0 & $a < c$\cr
{1\over \sqrt{a^2-c^2}} & $ a>c$\cr}
\end{displaymath}


\begin{displaymath}
\int_0^\infty J_0(ax)\sin (cx)\,dx=\cases{
{1\over \sqrt{c^2-a^2}} & $ a<c$\cr
\strut 0 & $a > c$,\cr}
\end{displaymath}

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


References

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




© 1996-9 Eric W. Weisstein
1999-05-26