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arXiv · 1907.05563

Elementary proofs of generalized continued fraction formulae for $e$

Zhentao Lu
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Abstract

In this short note we prove two elegant generalized continued fraction formulae $$e= 2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{2}{3+\cfrac{3}{4+\ddots}}}}$$ and $$e= 3+\cfrac{-1}{4+\cfrac{-2}{5+\cfrac{-3}{6+\cfrac{-4}{7+\ddots}}}}$$ using elementary methods. The first formula is well-known, and the second one is newly-discovered in arXiv:1907.00205 [cs.LG]. We then explore the possibility of automatic verification of such formulae using computer algebra systems (CAS's).

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Zhentao Lu. 2019-07-12. Elementary proofs of generalized continued fraction formulae for $e$. https://arxiv.org/abs/1907.05563

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