Functions and Analysis

2108 Submissions

[3] viXra:2108.0165 [pdf] submitted on 2021-08-30 22:31:23

Differential Coefficients at Corners and Division by Zero Calculus

Authors: Saburou Saitoh, Keitaroh Uchida
Comments: 5 Pages.

For a $C_1$ function $y=f(x)$ except for an isolated point $x=a$ having $f^\prime(a-0)$ and $f^\prime(a+0)$, we shall introduce its natural differential coefficient at the singular point $x=a$. Surprisingly enough, the differential coefficient is given by the division by zero calculus and it will give the gradient of the natural tangential line of the function $y=f(x)$ at the point $x=a$.
Category: Functions and Analysis

[2] viXra:2108.0148 [pdf] submitted on 2021-08-27 16:34:21

Two-Dimensional Fourier Transformations and Double Mordell Integrals II

Authors: Martin Nicholson
Comments: 6 Pages.

Several Fourier transforms of functions of two variables are calculated. They enable one to calculate integrals that contain trigonometric and hyperbolic functions and also evaluate certain double Mordell integrals in closed form.
Category: Functions and Analysis

[1] viXra:2108.0110 [pdf] submitted on 2021-08-21 20:23:36

Definition and Application of Anti-Factorial

Authors: Juan Elias Millas Vera
Comments: 3 Pages.

In this paper I want to show a new concept, the anti-factorial. This is the inverse operator of the factorial. I introduce a full (and necessary) new notation for this concept. The main idea is to develop an operator (notated by n¡) that is able of do the inverse form of an expanded number n to a contracted number k and if you do the factorial of k you will end up back at n, that is k!=n.
Category: Functions and Analysis