[12] **viXra:1808.0641 [pdf]**
*submitted on 2018-08-29 12:01:02*

**Authors:** Edigles Guedes

**Comments:** 5 Pages.

I derive some Ser's infinite product for exponential function and exponential of the digamma function; as well as an integral representation for the digamma function.

**Category:** Functions and Analysis

[11] **viXra:1808.0602 [pdf]**
*submitted on 2018-08-27 17:02:03*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 15 Pages.

In his 1859 paper, Bernhard Riemann used an integral equation to develop an explicit formula for estimating the number of prime numbers less than a given quantity. It is the
purpose of this present work to explore some of the properties of this integral equation.

**Category:** Functions and Analysis

[10] **viXra:1808.0576 [pdf]**
*submitted on 2018-08-26 10:55:02*

**Authors:** Adel Farhat, Anouar Ben Mabrouk

**Comments:** 20 Pages.

In the present paper, new multifractal analysis of vector valued Ahlfors type measures is developed. Mutual multifractal generalizations f fractal measures such as Hausdorff and packing have been introduced with associated dimensions. Essential properties of these measures have been shown using convexity arguments.

**Category:** Functions and Analysis

[9] **viXra:1808.0515 [pdf]**
*submitted on 2018-08-22 14:21:38*

**Authors:** Edigles Guedes

**Comments:** 5 Pages.

I derive an integral representation for the Barnes G-function among other things.

**Category:** Functions and Analysis

[8] **viXra:1808.0514 [pdf]**
*submitted on 2018-08-22 14:23:28*

**Authors:** Edigles Guedes

**Comments:** 2 Pages.

I derive an infinite product for gamma function and infinite series for log gamma function.

**Category:** Functions and Analysis

[7] **viXra:1808.0233 [pdf]**
*submitted on 2018-08-16 09:49:42*

**Authors:** Edigles Guedes

**Comments:** 4 Pages.

I derive some infinite product representations for the exponential function.

**Category:** Functions and Analysis

[6] **viXra:1808.0207 [pdf]**
*submitted on 2018-08-15 11:22:40*

**Authors:** Edigles Guedes

**Comments:** 9 Pages.

I derived an identity involving gamma functions and sine function at rational argument; hence, the representation of infinite product arose.

**Category:** Functions and Analysis

[5] **viXra:1808.0202 [pdf]**
*submitted on 2018-08-15 21:33:00*

**Authors:** Ruslan Sharipov

**Comments:** Designed for double sided printing, US Letter size, 35 pages, 5 color figures

Tetrahedral discretizations of the multielectron Schrödinger operator are suggested. They is based on tetrahedral triangulations of domains in R^{3}. Theoretical results proving that these discretizations are able to approximate energy levels of electrons in atoms and molecules are obtained.

**Category:** Functions and Analysis

[4] **viXra:1808.0154 [pdf]**
*submitted on 2018-08-12 21:21:29*

**Authors:** Seong Won Cha

**Comments:** 22 Pages.

We will show interesting properties of two-sided Laplace transform, mainly of positive even functions. Further, we will also prove that the Laguerre inequalities and generalized Laguerre inequalities are true and finally, the Riemann hypothesis is true.

**Category:** Functions and Analysis

[3] **viXra:1808.0136 [pdf]**
*replaced on 2018-08-27 11:22:36*

**Authors:** Edigles Guedes

**Comments:** 4 Pages.

I used an identity for cosine function involving finite product of the gamma functions; hence, the representation of infinite product arose.

**Category:** Functions and Analysis

[2] **viXra:1808.0116 [pdf]**
*submitted on 2018-08-10 07:35:26*

**Authors:** Edigles Guedes

**Comments:** 6 Pages.

I corrected the Theorem 21 of previous paper, obtaining an identity for sine function at rational argument involving finite sum of the gamma functions; hence, the representation of infinite product arose.

**Category:** Functions and Analysis

[1] **viXra:1808.0053 [pdf]**
*submitted on 2018-08-04 12:22:26*

**Authors:** Edigles Guedes

**Comments:** 6 Pages.

I derive an identity for the decomposition of the Pochhammer's symbol.

**Category:** Functions and Analysis