Functions and Analysis

2106 Submissions

[3] viXra:2106.0108 [pdf] submitted on 2021-06-19 20:06:05

Division by Zero Calculus in Figures - Our New Space Since Euclid -

Authors: Hiroshi Okumura, Saburou Saitoh
Comments: 54 Pages.

We will show in this paper in a self contained way that our basic idea for our space is wrong since Euclid, simply and clearly by using many simple and interesting figures.
Category: Functions and Analysis

[2] viXra:2106.0085 [pdf] submitted on 2021-06-14 08:40:03

On the State of Convergence of the Flint Hill Series

Authors: Theophilus Agama
Comments: 5 Pages.

In this paper we study the convergence of the flint hill series of the form \begin{align} \sum \limits_{n=1}^{\infty}\frac{1}{(\sin^2n) n^3}\nonumber \end{align}via a certain method. The method works essentially by erecting certain pillars sufficiently close to the terms in the series and evaluating the series at those spots. This allows us to relate the convergence and the divergence of the series to other series that are somewhat tractable. In particular we show that the convergence of the flint hill series relies very heavily on the condition that for any small $\epsilon>0$ \begin{align} \bigg|\sum \limits_{i=0}^{\frac{n+1}{2}}\sum \limits_{j=0}^{i}(-1)^{i-j}\binom{n}{2i+1} \binom{i}{j}\bigg|^{2s} \leq |(\sin^2n)|n^{2s+2-\epsilon}\nonumber \end{align}for some $s\in \mathbb{N}$.
Category: Functions and Analysis

[1] viXra:2106.0013 [pdf] submitted on 2021-06-03 17:07:17

New Notation in Series of Functions II

Authors: Juan Elias Millas Vera
Comments: 4 Pages.

In this paper we will see the next part of my theory of notation in series. Focusing on summation and productory we will do a defined explanation of an iterated serial operators.
Category: Functions and Analysis