13 citations · 21 across the 7 of their papers we have counts for
7 papers
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.
Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur
Leonhard Euler, Artur Diener, Alexander Aycock
This paper, along with E592 and E636, seems to consider the binomial expansion (1+z)^n in the case where z is complex. Euler even gives the sums of divergent series. The paper is t…