41 citations · 62 across the 8 of their papers we have counts for
8 papers
Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
Leonhard Euler
This translation has been withdrawn due to certain imperfections and mistakes, which are corrected in the version uploaded at The Euler Archive (see E65 at http://www.eulerarchive.…
Theorematum quorundam arithmeticorum demonstrationes
Leonhard Euler, Artur Diener, Alexander Aycock
Euler proves that the sum of two 4th powers can't be a 4th power and that the difference of two distinct non-zero 4th powers can't be a 4th power and Fermat's theorem that the equa…
Demonstratio insignis theorematis numerici circa uncias potestatum binomialium
Leonhard Euler, Artur Diener, Alexander Aycock
This paper is about the product z^q/(1 - z)^(q + 1)(1 + (z/(1 - z)))^p, Euler gives the Talylor-Series and takes a closer look at the coefficient.
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
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 f…
Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit
Leonhard Euler, Artur Diener, Alexander Aycock
Euler gives a continued fraction representation of (1 + x)n. involving 1,3,5,7,... and n^2-1,n^2-4,n^3-9,... and squares of z, for x=2y and y=z/(1-z). He evaluates this continued f…
Disquitiones analyticae super evolutione potestatis trinomialis (1+x+xx)^n
Leonhard Euler, Artur Diener, Alexander Aycock
Euler investigates the Taylorseries of (1+x+xx)^n and uses the results to evaluates some integrals which are today often proved with the calculus of residues.