雅可比多项式积积分的一个渐近公式

arXiv: Classical Analysis and ODEs Pub Date : 2020-10-21 DOI:10.31390/JOSA.1.4.08

Maxim S. Derevyagin, Nicholas Juricic

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引用次数: 1

摘要

我们对勒让德多项式积的积分改写了拜尔利公式。然后我们将这一思想应用于雅可比多项式的情况。然后，利用该公式导出了雅可比多项式积积分的渐近公式。该渐近公式与第一作者和Jeff Geronimo最近为另一种情况得到的类似公式相似。因此，它表明，这种渐近的行为是相当普遍的积分的正交多项式的乘积。

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An Asymptotic Formula for Integrals of Products of Jacobi Polynomials

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.

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arXiv: Classical Analysis and ODEs

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