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- Publications
- Influence
Euler and the Gammafunction.
- A. Aycock
- Mathematics
- 5 August 2019
We review Euler's idea on the Gammafunction. We will explain, how Euler obtained them and how Euler's ideas anticipate more modern approaches and theories. Furthermore, some questions asked by Euler… Expand
Theoremata arithmetica nova methodo demonstrata
- L. Euler, Artur Diener, A. Aycock
- Mathematics
- 9 March 2012
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 smallest power x^n… Expand
Translation of the C.J. Malmstén's paper De integralibus quibusdam definitis, seriebusque infinitis
- A. Aycock
- Mathematics
- 16 September 2013
In 1846 (published in the Crelle Journal für die reine und angewandte Mathematik) the nowadays widely unknown Swedish mathematician C. J. Malmstén wrote his quite remarkable paper "De integralibus… Expand
Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum.
This is the translation of Euler's Latin textbook Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum (second volume) into English.
Evolutio producti infiniti (1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5) etc. in seriem simplicem
- L. Euler, Artur Diener, A. Aycock
- Mathematics
- 1 February 2012
This paper does exactly what the title says it does. It expands the given series to arrive at the familiar "pentagonal number" expansion, also known as the pentagonal number theorem, and recalls its… Expand
On proving some of Ramanujan's formulas for $\frac{1}{\pi}$ with an elementary method
- A. Aycock
- Mathematics
- 4 September 2013
In this paper we want to prove some formulas listed by S. Ramanujan in his paper "Modular equations and approximations to $\pi$" \cite{24} with an elementary method.
Proof of some conjectured formulas for 1/pi by Z.-W. Sun
- G. Almkvist, A. Aycock, appendix by Arne Meurman
- Mathematics
- 14 December 2011
Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in… Expand
Explicit formulas for orthogonal polynomials derived from their difference equation
- A. Aycock
- Mathematics
- 20 June 2015
We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.
Notes and Remarks on certain logarithmic integrals
- A. Aycock
- Mathematics
- 22 July 2013
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain… Expand
Bourlet's Theorem for the product of differential operators, an application of the operator method and a proof for $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$, that Euler missed, derived from…
- A. Aycock
- Mathematics
- 20 June 2015
We give another proof for \[ \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6} \] that basically follows from the theory of difference equations.
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