Disquitiones analyticae super evolutione potestatis trinomialis (1+x+xx)^n
History and Overview
2012-02-02 v1
Abstract
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.
Cite
@article{arxiv.1202.0028,
title = {Disquitiones analyticae super evolutione potestatis trinomialis (1+x+xx)^n},
author = {Leonhard Euler and Artur Diener and Alexander Aycock},
journal= {arXiv preprint arXiv:1202.0028},
year = {2012}
}
Related papers
View all related →
History and Overview · Mathematics
Demonstratio insignis theorematis numerici circa uncias potestatum binomialium
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-02
History and Overview · Mathematics
General observations on series whose terms proceed as the sines and cosines of multiples of angles
Leonhard Euler
2007-09-06
History and Overview · Mathematics
Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-02
History and Overview · Mathematics
Nova demonstratio, quod evolutio potestatum binomii Newtoniana etiam pro exponentibus fractis valeat
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-02
History and Overview · Mathematics
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
2012-02-02
History and Overview · Mathematics
On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc
Leonhard Euler
2007-05-23
History and Overview · Mathematics
A succinct method for investigating the sums of infinite series through differential formulae
Leonhard Euler
2007-05-23
History and Overview · Mathematics
Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-02
History and Overview · Mathematics
De seriebus divergentibus
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-08
History and Overview · Mathematics
Various analytic observations on combinations
Leonhard Euler
2007-11-26
History and Overview · Mathematics
A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
Leonhard Euler
2007-05-23
History and Overview · Mathematics
Variae considerationes circa series hypergeometricas
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-02
History and Overview · Mathematics
Expansion of the infinite product $(1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5)(1-x^6)$ etc. into a simple series
Leonhard Euler, Jordan Bell
2009-08-31
History and Overview · Mathematics
Observations on continued fractions
Leonhard Euler, Alexander Aycock
2018-08-22
History and Overview · Mathematics
A demonstration of a theorem on the order observed in the sums of divisors
Leonhard Euler, Jordan Bell
2009-07-30
Classical Analysis and ODEs · Mathematics
Expansion Series of $f(x)=x^x$ And Characterization of its Coefficients
Oliver Planes
2014-11-07
History and Overview · Mathematics
On the remarkable properties of the pentagonal numbers
Leonhard Euler
2007-05-23
History and Overview · Mathematics
Euler and the Legendre Polynomials
Alexander Aycock
2023-09-01
Exactly Solvable and Integrable Systems · Physics
Leonard Euler: addition theorems and superintegrable systems
A V Tsiganov
2011-09-06
Combinatorics · Mathematics
Eulerian polynomials and the alternating sum of excedances
Jean-Christophe Pain
2026-03-25
Combinatorics · Mathematics
Th\'eorie G\'eom\'etrique des Polyn\^omes Eul\'eriens
Dominique Foata, Marcel-Paul Schützenberger
2007-05-23
Computational Physics · Physics
Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials
Riccardo Borghi
2010-02-18
History and Overview · Mathematics
De transformatione seriei divergentis 1 - mx + m(m+n)x^2 - m(m+n)(m+2n)x^3 + etc. in fractionem continuam
Leonhard Euler, Artur Diener, Alexander Aycock
2012-02-01
History and Overview · Mathematics
Observations on two fourth powers whose sum is equal to the sum of two other fourth powers
Leonhard Euler, Jordan Bell
2009-08-10
History and Overview · Mathematics
Specimen transformationis singularis serierum
Leonhard Euler, Artur Diener, Alexander Aycock
2012-01-27