52 citations · 82 across the 7 of their papers we have counts for
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Euler and the Legendre Polynomials
Alexander Aycock
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the…
Euler's First Proof of Stirling's Formula
Alexander Aycock
We present a proof given by Euler in his paper {\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination…
On Euler's Solution of the simple Difference Equation
Alexander Aycock
In this note we will discuss Euler's solution of the simple difference equation that he gave in his paper{\it ``De serierum determinatione seu nova methodus inveniendi terminos gen…
Euler and the Duplication Formula for the Gamma-Function
Alexander Aycock
We show how the formulas in paper Variae considerationes circa series hypergeometricas written by Euler imply the duplication formula for the Gamma-function. This paper can be seen…
Theoremata arithmetica nova methodo demonstrata
Leonhard Euler, Artur Diener, Alexander Aycock
Euler presents a third proof of the Fermat theorem, the one that lets us call it the Euler-Fermat theorem. This seems to be the proof that Euler likes best. He also proves that the…
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…