# Functions and Analysis

## 1411 Submissions

[3] **viXra:1411.0560 [pdf]**
*submitted on 2014-11-25 09:47:20*

### On Filter Alpha-Convergence and Exhaustiveness of Function Nets in Lattice Groups and Applications

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 8 Pages.

We consider (strong uniform) continuity of the
limit of a pointwise convergent net of lattice
group-valued functions, (strong weak)
exhaustiveness and (strong)
alpha-convergence with respect to a pair
of filters, which in the setting of nets are
more natural than the corresponding notions
formulated with respect to a single filter. Some
comparison results are given between such concepts, in connection with suitable properties of filters. Moreover, some modes of filter
(strong uniform) continuity for lattice
group-valued functions are investigated, giving
some characterization. As an application, we get
some Ascoli-type theorem in an abstract setting,
extending earlier results to the context of filter
alpha-convergence.

**Category:** Functions and Analysis

[2] **viXra:1411.0548 [pdf]**
*submitted on 2014-11-23 10:10:13*

### New Infnite Series and Integral Representations for Error Function

**Authors:** Edigles Guedes

**Comments:** 9 pages.

I proved some infinity series power and integral representations for error function
and relations for special functions.

**Category:** Functions and Analysis

[1] **viXra:1411.0228 [pdf]**
*replaced on 2014-11-23 09:56:15*

### Infinite Serie and Integral Representations for Bessel Function of the First Kind J_v(z)

**Authors:** Edigles Guedes

**Comments:** 7 pages

I prove one expansion of infinite serie and some integral representations for Bessel function of the first kind.

**Category:** Functions and Analysis