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Mathematics of Computation

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A Legendre polynomial integral

Author: James L. Blue
Journal: Math. Comp. 33 (1979), 739-741
MSC: Primary 65D30; Secondary 33A45
MathSciNet review: 521287
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Abstract: Let $ \{ {P_n}(x)\} $ be the usual Legendre polynomials. The following integral is apparently new.

$\displaystyle \int _0^1{P_n}(2x - 1)\log \frac{1}{x}dx = \frac{{{{( - 1)}^n}}}{{n(n + 1)}}\quad {\text{for}}\;n \geqslant 1.$

It has an application in the construction of Gauss quadrature formulas on (0, 1) with weight function $ \log (1/x)$.

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Article copyright: © Copyright 1979 American Mathematical Society

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