Speculationes super formula integrali ∫ (xⁿdx)/\surd(aa-2bx+cxx), ubi simul egregiae observationes circa fractiones continuas occurrunt

2012/01/31 by Leonhard Euler, Euler, Leonhard, Artur Diener +3
Earth and Planetary Sciences · Mathematics · #FOS: Mathematics #Geophysics and Gravity Measurements #History and Overview (math.HO) #Mathematical functions and polynomials #Numerical methods for differential equations #math.HO

paper · pdf · doi:10.48550/arxiv.1202.0037

arxiv created 2012/01/31 · openalex publication_date 2012/01/31 · arxiv updated 2012/02/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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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