TOPICS
Search

Lommel's Integrals


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)]

and

 intx[J_n(alphax)]^2dx 
 =1/2x^2{[J_n(alphax)]^2-J_(n-1)(alphax)J_(n+1)(alphax)},

where J_n(x) is a Bessel function of the first kind.


See also

Bessel Function of the First Kind

Explore with Wolfram|Alpha

References

Bowman, F. Introduction to Bessel Functions. New York: Dover, p. 101, 1958.

Referenced on Wolfram|Alpha

Lommel's Integrals

Cite this as:

Weisstein, Eric W. "Lommel's Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LommelsIntegrals.html

Subject classifications