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

Alexander Aycock; Artur Diener; Leonhard Euler

arxiv: 1202.0037 · v1 · pith:RZEFP36Pnew · submitted 2012-01-31 · 🧮 math.HO

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 This is my paper

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keywords euleraa-2bxarctancircacontinuascontinuedegregiaeevaluates

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

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