De transformatione seriei divergentis 1 - mx + m(m+n)x^2 - m(m+n)(m+2n)x^3 + etc. in fractionem continuam

Alexander Aycock; Artur Diener; Leonhard Euler

arxiv: 1201.6687 · v1 · pith:J7FNZWXKnew · submitted 2012-01-31 · 🧮 math.HO

De transformatione seriei divergentis 1 - mx + m(m+n)x² - m(m+n)(m+2n)x³ + etc. in fractionem continuam

Leonhard Euler , Artur Diener , Alexander Aycock This is my paper

classification 🧮 math.HO

keywords eulerseriescontinuamcontinuedderviesdivergentdivergentisexpansion

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In this paper, Euler transforms the divergent series in the title, and thereby dervies the well known continued fraction expansion for pi/4 from Leibniz's series. The paper is translated from Euler's Latin originial into German.

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De transformatione seriei divergentis 1 - mx + m(m+n)x² - m(m+n)(m+2n)x³ + etc. in fractionem continuam

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