论文标题
关于Jacobi多项式产物积分的渐近公式的注释
A note on an asymptotic formula for integrals of products of Jacobi polynomials
论文作者
论文摘要
我们将旁观者的公式用于Legendre多项式产品的积分。然后，我们将这个想法采用到雅各比多项式的情况下。之后，我们使用该公式来得出渐近公式，以用于雅各比多项式产物的积分。渐近公式类似于第一作者最近获得的类似公式，而杰夫·杰罗尼莫（Jeff Geronimo）则针对另一种情况。因此，这表明这种渐近行为对于正交多项式产品的积分是相当通用的。
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.
