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

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

2012-01-31

arxiv.org/abs/1202.0037v1

Mathematics

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Scientific paper

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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