# Functions and Analysis

## 1903 Submissions

[3] **viXra:1903.0326 [pdf]**
*submitted on 2019-03-17 07:33:40*

### Espil's High Power Partial Fraction Decomposition Theorem.

**Authors:** Federico Espil

**Comments:** 6 Pages.

The problem of fraction decomposition it's easy to solve by using the cover up method, when there are no repeated linear factors in the denominator .
Nevertheless it could turn into a hard work if these factors are raised to a high power, where the cover up method doesn't work. This technique shows how to calculate these coefficients without solving large systems of equations with a clever rearrangement of the numerator.

**Category:** Functions and Analysis

[2] **viXra:1903.0315 [pdf]**
*submitted on 2019-03-18 05:25:09*

### Differential Equation

**Authors:** Fayowole David Ayadi

**Comments:** 3 Pages.

The laws of Physics and some other related courses are generally written as differential equations. Therefore, all of science
and engineering use differential equations to some extent. A good knowledge of differential equations will be an integral
part of your study in science and/or engineering classes. You can think of mathematics as the language of science, and
differential equations are one of the most important parts of this language as far as science and engineering are concerned.

**Category:** Functions and Analysis

[1] **viXra:1903.0231 [pdf]**
*submitted on 2019-03-12 22:17:08*

### Espil's Theorem Corollary.

**Authors:** Federico Espil

**Comments:** 5 Pages.

Shortly from the Espil's theorem, we can derive the generalized Dirichlet
integral for any natural value when the hole integrand is raised to the n-th power.

**Category:** Functions and Analysis