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math.HOJan 31, 2012
8
citations (OpenAlex)
authors
  • Leonhard Euler
  • Artur Diener
  • Alexander Aycock
arXiv abstractPDF
paper

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

arXiv:1201.6687

Abstract

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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  • Lattice paths and branched continued fractions. III. Generalizations of the Laguerre, rook and Lah polynomials
  • A remark on continued fractions for permutations and D-permutations with a weight −1 per cycle
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