  We recast Byerly's formula for integrals of products of Legendre polynomials.
Then we adopt the idea to the case of Jacobi polynomials. After that, we use
the formula to derive an asymptotic formula for integrals of products of Jacobi
polynomials. The asymptotic formula is similar to an analogous one recently
obtained by the first author and Jeff Geronimo for a different case. Thus, it
suggests that such an asymptotic behavior is rather generic for integrals of
products of orthogonal polynomials.
