[2] **viXra:1004.0053 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, Mircea Eugen Șelariu

**Comments:** 10 pages

This article presents two methods, in parallel, of solving more complex integrals, among
which is the Poisson's integral, in order to emphasize the obvious advantages of a new method
of integration, which uses the supermathematics circular ex-centric functions.
We will specially analyze the possibilities of easy passing/changing of the supermathematics
circular ex-centric functions of a centric variable α to the same functions of ex-centric variable &theta.
The angle α is the angle at the center point O(0,0), which represents the centric variable and θ
is the angle at the ex-center E(k,ε), representing the ex-centric variable. These are the angles
from which the points W_{1} and W_{2} are visible on the unity circle - resulted from the intersection
of the unity/trigonometric circle with the revolving straight line d around the ex-centric
E(k,&epsilon) - from O and from E, respectively.

**Category:** Functions and Analysis

[1] **viXra:1004.0014 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

As a consequence of the Integral Test we find a triple inequality which bounds up and
down both a series with respect to its corresponding improper integral, and reciprocally
an improper integral with respect to its corresponding series.

**Category:** Functions and Analysis