# Functions and Analysis

## 1711 Submissions

[4] **viXra:1711.0356 [pdf]**
*submitted on 2017-11-18 15:54:02*

### On the Attempt to Use a Stochastic Interpretation to Compute the Trace of a Regular Representation U on X = Ak/k*

**Authors:** Matanari Shimoinuda

**Comments:** 12 Pages.

The group X, which is proposed by A.Connes, is an interesting thing for number theory. Let's think of the trace of a regular representation U on X of the idele class. However it is hard to compute it since X is non-compact. In this article, we try to show that the trace is computable.

**Category:** Functions and Analysis

[3] **viXra:1711.0298 [pdf]**
*submitted on 2017-11-13 20:01:20*

### Some Infinite "Continuous" Products Over the Interval (0,1)

**Authors:** D Williams

**Comments:** 3 Pages.

Some "continuous" (that is, over real numbers in the interval (0,1)) infinite products are given with their finite product approximations. THESE PRODUCTS DESERVE MORE STUDY.

**Category:** Functions and Analysis

[2] **viXra:1711.0297 [pdf]**
*submitted on 2017-11-13 20:05:52*

### Dx-less Integrals

**Authors:** D Williams

**Comments:** 3 Pages.

Some examples of dx-less integrals are given with their finite sum approximations. They appear to have use in estimating long-term values of certain stochastic recursive functions. A request is made for determining convergence of such integrals.

**Category:** Functions and Analysis

[1] **viXra:1711.0257 [pdf]**
*submitted on 2017-11-09 15:57:32*

### Improvement on Stirling's Formula for n! Using Product Integrals

**Authors:** D Williams

**Comments:** 10 Pages.

An improved version of Stirling's Formula (which I call Neylon's Approximation) for n! is constructed using Product Integrals.

**Category:** Functions and Analysis