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Further Extensions of a Legendre Function Integral

Henry E. Fettis
Mathematics of Computation
Vol. 45, No. 172 (Oct., 1985), pp. 549-552
DOI: 10.2307/2008144
Stable URL: http://www.jstor.org/stable/2008144
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Further Extensions of a Legendre Function Integral
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Abstract

The integral $$\int^1_z \bigg(\frac{1 - t}{2}\bigg)^{\beta - 1}\bigg(\frac{1 - t}{1 + t}\bigg)^{\mu/2} \ln\bigg(\frac{1 - t}{2}\bigg)P{}_{\nu - 1}^\mu(t) dt$$ is evaluated as a hypergeometric function for arbitrary values of "$\nu$", "$\mu$", $-1 \leqslant z \leqslant 1$, and $\mathrm{Re}(\beta) > 0$.

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