Further extensions of a Legendre function integral

Fettis, Henry E.

doi:10.1090/S0025-5718-1985-0804943-6

Further extensions of a Legendre function integral
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by Henry E. Fettis PDF

Math. Comp. 45 (1985), 549-552 Request permission

Abstract:

The integral \[ \int _z^1 {{{\left ( {\frac {{1 - t}}{2}} \right )}^{\beta - 1}}{{\left ( {\frac {{1 - t}}{{1 + t}}} \right )}^{\mu /2}}\ln \left ( {\frac {{1 - t}}{2}} \right )P_{\nu - 1}^\mu (t)\;dt} \] is evaluated as a hypergeometric function for arbitrary values of $\nu$, $\mu$, $- 1 \leqslant z \leqslant 1$, and $\operatorname {Re} (\beta ) > 0$.

References

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