The two integrals involving Bessel functions of the first kind given by
![(alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx
=x[betaJ_(n-1)(betax)J_n(alphax)-alphaJ_(n-1)(alphax)J_n(betax)]](/images/equations/LommelsIntegrals/NumberedEquation1.svg) |
and
![intx[J_n(alphax)]^2dx
=1/2x^2{[J_n(alphax)]^2-J_(n-1)(alphax)J_(n+1)(alphax)},](/images/equations/LommelsIntegrals/NumberedEquation2.svg) |
where 
is a Bessel function of the first kind.
Lommel's Integrals
See also
Bessel Function of the First KindExplore with Wolfram|Alpha
References
Bowman, F. Introduction to Bessel Functions. New York: Dover, p. 101, 1958.Referenced on Wolfram|Alpha
Lommel's IntegralsCite this as:
Weisstein, Eric W. "Lommel's Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LommelsIntegrals.html