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Mathematics of Computation

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Further extensions of a Legendre function integral

Author: Henry E. Fettis
Journal: Math. Comp. 45 (1985), 549-552
MSC: Primary 33A30
MathSciNet review: 804943
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Abstract: The integral

$\displaystyle \int_z^1 {{{\left( {\frac{{1 - t}}{2}} \right)}^{\beta - 1}}{{\le... ...ight)}^{\mu /2}}\ln \left( {\frac{{1 - t}}{2}} \right)P_{\nu - 1}^\mu (t)\;dt} $

is evaluated as a hypergeometric function for arbitrary values of $ \nu $, $ \mu $, $ - 1 \leqslant z \leqslant 1$, and $ \operatorname{Re} (\beta ) > 0$.

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Keywords: Jacobi polynomials, Legendre functions, hypergeometric functions, $ \Gamma $-functions, definite integrals, beta transform
Article copyright: © Copyright 1985 American Mathematical Society

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