Lemma 5.2 . [024D]

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Lemma 5.2.

For $x\geq 1$ we have

\int_{1}^{x}(1-y^{-2})^{-1/n}dy=x\,_{2}F_{1}[-\frac{1}{2},\frac{1}{n};\frac{1}{2};x^{-2}]-\,_{2}F_{1}[-\frac{1}{2},\frac{1}{n};\frac{1}{2};1].