# Functions and Analysis

## 2001 Submissions

 viXra:2001.0387 [pdf] replaced on 2020-01-20 13:04:21

### Refutation of Riemann’s Definition of Integrals for a Cheating Runner

Authors: Colin James III

We evaluate six equations which are not tautologous. This refutes the conjecture of Riemann’s definition of integrals for a cheating runner before the integral is invoked to form a non tautologous fragment of the universal logic VŁ4.
Category: Functions and Analysis

 viXra:2001.0376 [pdf] submitted on 2020-01-20 10:09:54

### On a Certain Identity Involving the Gamma Function

Authors: Theophilus Agama

The goal of this paper is to prove the identity \begin{align}\sum \limits_{j=0}^{\lfloor s\rfloor}\frac{(-1)^j}{s^j}\eta_s(j)+\frac{1}{e^{s-1}s^s}\sum \limits_{j=0}^{\lfloor s\rfloor}(-1)^{j+1}\alpha_s(j)+\bigg(\frac{1-((-1)^{s-\lfloor s\rfloor +2})^{1/(s-\lfloor s\rfloor +2)}}{2}\bigg)\nonumber \\ \bigg(\sum \limits_{j=\lfloor s\rfloor +1}^{\infty}\frac{(-1)^j}{s^j}\eta_s(j)+\frac{1}{e^{s-1}s^s}\sum \limits_{j=\lfloor s\rfloor +1}^{\infty}(-1)^{j+1}\alpha_s(j)\bigg)=\frac{1}{\Gamma(s+1)},\nonumber \end{align}where \begin{align}\eta_s(j):=\bigg(e^{\gamma (s-j)}\prod \limits_{m=1}^{\infty}\bigg(1+\frac{s-j}{m}\bigg)\nonumber \\e^{-(s-j)/m}\bigg)\bigg(2+\log s-\frac{j}{s}+\sum \limits_{m=1}^{\infty}\frac{s}{m(s+m)}-\sum \limits_{m=1}^{\infty}\frac{s-j}{m(s-j+m)}\bigg), \nonumber \end{align}and \begin{align}\alpha_s(j):=\bigg(e^{\gamma (s-j)}\prod \limits_{m=1}^{\infty}\bigg(1+\frac{s-j}{m}\bigg)e^{-(s-j)/m}\bigg)\bigg(\sum \limits_{m=1}^{\infty}\frac{s}{m(s+m)}-\sum \limits_{m=1}^{\infty}\frac{s-j}{m(s-j+m)}\bigg),\nonumber \end{align}where $\Gamma(s+1)$ is the Gamma function defined by $\Gamma(s):=\int \limits_{0}^{\infty}e^{-t}t^{s-1}dt$ and $\gamma =\lim \limits_{n\longrightarrow \infty}\bigg(\sum \limits_{k=1}^{n}\frac{1}{k}-\log n\bigg)=0.577215664\cdots$ is the Euler-Mascheroni constant.
Category: Functions and Analysis

 viXra:2001.0375 [pdf] submitted on 2020-01-19 11:11:06

### A Useful Result About the Zeros of Riemann’s Hypothesis:

Authors: Louiz Akram
Comments: 6 Pages. This is a better corrected work from a previous work.

Motivated by many scientific articles attacking the use of Riemann’s hypothesis, I made a very useful work about it by proving that the zeros of zeta when the variable real part is smaller than 1/2 and thus of Riemann’s Hypothesis aren’t images of the divergent function series . In this proof, I didn't suppose that zeta is convergent, but I supposed that the zero is among the images of a given complex number, since zeta can only be a relation when it doesn't converge.
Category: Functions and Analysis

 viXra:2001.0360 [pdf] submitted on 2020-01-18 10:14:47

### A Runner Cheating Thanks to Riemann:

Authors: Louiz Akram
Comments: 2 Pages. This is a better corrected work from a previous work about integrals.

Pure mathematics should be used very carefully when applying it to many fields that have special considerations and special axioms. I used a simple example of runners waiting for the start of a race. I concluded thanks to Riemann’s definition of integrals that a runner can cheat in order to win. The demonstration in this paper is very simple but the analogy of the proposed example with many fields can make the researcher be careful when using the definition of Riemann for the integrals.
Category: Functions and Analysis

 viXra:2001.0342 [pdf] submitted on 2020-01-18 07:05:13

### Solve Equations.(Τhe Generalized Theorem)

Authors: Nikos Mantzakouras

While all the approximate methods mentioned or others that exist, give some specific solutions of the generalized transcendental equations or even polynomial, cannot resolve them completely. "What we ask when we solve a generalized transcendental equation or polyonomial, is to find the total number of roots and not separate sets of roots in some random or specified this time. Mainly because this, too many categories transcendental equations have infinite number of solutionsin the complex whole " There are some particular equations or Logarithmic functions Trigonometric functions which solve particular problems in Physics, and mostly need the generalized solution. This is now the theory G.R.LE, to deal with the help of Super Simple geometric functions, or interlocking with very satisfactory answer to all this complex problem.
Category: Functions and Analysis

 viXra:2001.0222 [pdf] submitted on 2020-01-13 08:26:54

### The Fuzzy Probabilities

Authors: Antoine Balan
Comments: 1 page, written in english

We propose to introduce a measure in the theory of fuzzy sets, calling this notion the fuzzy probabilities.
Category: Functions and Analysis

 viXra:2001.0205 [pdf] submitted on 2020-01-11 13:28:49

### AMASING proof of the STRONG Riemman Hypothes (Gnembon's Theorem)

Authors: Gnet Gnembon

Le Riemman Hypothosos is an hypothes that has existsence sinse Reimman (1837). He said so: The zero of this fonktion $\sum_{n=1}^\infty1/k^z$ is 1/2 real. We now prov this and its stronger we be rich million prise thankyou clay intitut we want double prise sinse we prov strong hopotosos. We call it GNEMBON's THEOREM.
Category: Functions and Analysis

 viXra:2001.0103 [pdf] submitted on 2020-01-07 04:56:29

### Integrals of Entire, Meromorphic and Subharmonic Functions on Small Sets of the Positive Semiaxis

Authors: Bulat N. Khabibullin
We will give a generalization of the division by zero calculus to differentiable functions and its basic properties. Typically, we can obtain l'Hôpital's theorem versions and some deep properties on the division by zero. Division by zero, division by zero calculus, differentiable, analysis, Laurent expansion, l'Hôpital's theorem, $1/0=0/0=z/0=\tan(\pi/2) =\log 0 =0, (z^n)/n = \log z$ for $n=0$, $e^{(1/z)} = 1$ for $z=0$.