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arXiv · 1202.0037

Speculationes super formula integrali {\int} (x^ndx)/{\surd}(aa-2bx+cxx), ubi simul egregiae observationes circa fractiones continuas occurrunt

Leonhard Euler·Artur Diener·Alexander Aycock
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Abstract

Euler evaluates the integrals in the title and recognizes a recursion between them, which he then uses to give continued fractions for the log and arctan. The paper is translated from Euler's Latin original into German.

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Leonhard Euler, Artur Diener, Alexander Aycock. 2012-01-31. Speculationes super formula integrali {\int} (x^ndx)/{\surd}(aa-2bx+cxx), ubi simul egregiae observationes circa fractiones continuas occurrunt. https://arxiv.org/abs/1202.0037

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