关于勒让德多项式积分的推广
Generalizations of an integral for Legendre polynomials by Persson and Strang
摘要：
Ewesson和Strang（2003）计算了平方奇数次勒让德多项式除以x^2的[-1，1]上的积分等于2。我们考虑了正交多项式关于一般偶正交测度的类似积分，Gegenbauer和Hermite多项式作为显式特殊情况。接下来，经过二次变换，我们被引导到一般的非对称的情况下，雅可比和Laguerre多项式作为显式的特殊情况。在这种情况下，也会出现不确定求和的例子。本文的结论与哈恩多项式的早期结果的推广。为了达到相对较好的明确评价，必须进行一些调整。
英文摘要：
Persson and Strang (2003) evaluated the integral over [-1,1] of a squared odd degree Legendre polynomial divided by x^2 as being equal to 2. We consider a similar integral for orthogonal polynomials with respect to a general even orthogonality measure, with Gegenbauer and Hermite polynomials as explicit special cases. Next, after a quadratic transformation, we are led to the general nonsymmetric case, with Jacobi and Laguerre polynomials as explicit special cases. Examples of indefinite summation also occur in this context. The paper concludes with a generalization of the earlier results for Hahn polynomials. There some adaptations have to be made in order to arrive at relatively nice explicit evaluations.
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