ﻻ يوجد ملخص باللغة العربية
This is the translation of Leonhard Eulers paper De Seriebus divergentibus written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example $1!-2!+3!-text{etc.}$ and uses different methods to sum it. He finds a value of about $0.59...$.
E661 in the Enestrom index. This was originally published as Variae considerationes circa series hypergeometricas (1776). In this paper Euler is looking at the asymptotic behavior of infinite products that are similar to the Gamma function. He look
Let $mathscr{X}$ be the set of positive real sequences $x=(x_n)$ such that the series $sum_n x_n$ is divergent. For each $x in mathscr{X}$, let $mathcal{I}_x$ be the collection of all $Asubseteq mathbf{N}$ such that the subseries $sum_{n in A}x_n$ is
A translation of Kummer`s paper On certain definite integrals and infinite series
Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelles Journal (1829) with numerous typographical corrections, and added a completed bibliography. Dirichlet
This is an English translation of the Latin original De summa seriei ex numeris primis formatae ${1/3}-{1/5}+{1/7}+{1/11}-{1/13}-{1/17}+{1/19}+{1/23}-{1/29}+{1/31}-$ etc. ubi numeri primi formae $4n-1$ habent signum positivum formae autem $4n+1$ sign