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