| viXra.org > Functions and Analysis > 2001 |
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| viXra.org > Functions and Analysis > 2001 |
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[10] viXra:2001.0603 [pdf] replaced on 2022-01-28 11:04:31
Authors: Richard J. Mathar
Comments: 12 Pages. Version 2 includes formula for solid angle of the on-axis ellipse
The solid angle covered by a rectangular plate of length a
and width b at a distance d to the observer is calculated.
[vixra:2001.0603]
Category: Functions and Analysis
[9] viXra:2001.0590 [pdf] submitted on 2020-01-27 13:54:24
Authors: Bulat N. Khabibullin
Comments: 5 Pages.
Let u be an arbitrary subharmonic function of finite order on the complex plane. We construct a nonzero entire function f such that ln|f| does not exceed the function u everywhere outside some very small exceptional set E.
Category: Functions and Analysis
[8] viXra:2001.0586 [pdf] submitted on 2020-01-27 16:28:38
Authors: Saburou Saitoh
Comments: 9 Pages. I am writing a book on the division by zero and so I am asking for kind suggestions and comments on the topics.
Based on a preprint survey pape, we will give a fundamental relation among the basic concepts of division by zero calculus, derivatives and Laurent's expansion as a direct extension of the preprint which gave the generalization of the division by zero calculus to differentiable functions.
In particular, we will find a new viewpoint and applications to the Laurent expansion, in particular, to residures in the Laurent expansion.
$1/0=0/0=z/0=\tan(\pi/2) =\log 0 =0, (z^n)/n = \log z$ for $n=0$, $e^{(1/z)} = 1$ for $z=0$.
Category: Functions and Analysis
[7] viXra:2001.0376 [pdf] submitted on 2020-01-20 10:09:54
Authors: Theophilus Agama
Comments: 8 Pages.
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
[6] viXra:2001.0360 [pdf] replaced on 2022-12-07 01:55:18
Authors: Louiz Akram
Comments: 3 Pages.
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
[5] viXra:2001.0342 [pdf] submitted on 2020-01-18 07:05:13
Authors: Nikos Mantzakouras
Comments: 22 Pages.
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
[4] viXra:2001.0222 [pdf] submitted on 2020-01-13 08:26:54
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
[3] viXra:2001.0205 [pdf] submitted on 2020-01-11 13:28:49
Authors: Gnet Gnembon
Comments: 3 Pages.
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
[2] viXra:2001.0103 [pdf] submitted on 2020-01-07 04:56:29
Authors: Bulat N. Khabibullin
Comments: 3 Pages. in Russian
In this note, we announce the results on estimates of integrals of entire, meromorphic, and subharmonic functions on small subsets of the positive semiaxis. These results develop one classical theorem of R. Nevanlinna and the well-known lemmas on small arcs or intervals of A. Edrei, W.H.J. Fuchs, A.F. Grishin, M.L. Sodin and T.I. Malyutina.
Category: Functions and Analysis
[1] viXra:2001.0091 [pdf] submitted on 2020-01-06 17:52:07
Authors: Saburou Saitoh
Comments: 10 Pages. Based on the preprint survey paper, 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
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 $z=0$.
Category: Functions and Analysis
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