Functions and Analysis

2203 Submissions

[6] viXra:2203.0155 [pdf] submitted on 2022-03-26 04:24:39

Derivative of a Sequence at Infinity

Authors: Josef Bukac
Comments: 13 Pages.

When a sequence of real numbers is convergent to some finite number, we may approximate the members of the sequence by its limit provided the subscript is large. But we may want a higher accuracy. If we know the speed of convergence, we define a derivative of the sequence at infinity. We also define the second derivative which enables us even better approximations.
Category: Functions and Analysis

[5] viXra:2203.0136 [pdf] submitted on 2022-03-24 23:26:10

Triangular A-Statistical Approximation by Double Sequences of Positive Linear Operators

Authors: Carlo Bardaro, Antonio Boccuto, Kamil Demirci, Ilaria Mantellini, Sevda Orhan
Comments: 21 Pages.

In the present paper we introduce a new type of statistical convergence for double sequences called triangular A-statistical convergence and we show that triangular A-statistical convergence and A-statistical convergence overlap, neither contains the other. Also, we give a Korovkintype approximation theorem using this new type of convergence. Finally we give some further developments.
Category: Functions and Analysis

[4] viXra:2203.0072 [pdf] replaced on 2022-03-20 19:40:44

Matrix Exponential Computational Algorithm

Authors: Kenneth C. Johnson
Comments: 11 Pages.

A numerical algorithm for the matrix exponential is developed, based on the scale-and-square method applied to a Padé approximant for small-norm matrices.
Category: Functions and Analysis

[3] viXra:2203.0071 [pdf] submitted on 2022-03-14 16:19:16

Amazing Formulas Related to pi

Authors: Edgar Valdebenito
Comments: 10 Pages.

In this note we give some formulas related to Pi.
Category: Functions and Analysis

[2] viXra:2203.0070 [pdf] submitted on 2022-03-14 21:24:32

What is the Value of the Function X/x at X=0? What is 0/0?

Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 9 Pages.

It will be a very pity that we have still confusions on the very famous problem on 0/0 and the value of the elementary function of x/x at x=0. In this note, we would like to discuss the problems in some elementary and self contained way in order to obtain some good understanding for some general people.
Category: Functions and Analysis

[1] viXra:2203.0001 [pdf] submitted on 2022-03-01 20:27:07

One Century since Bergman, Szego and Bochner on Reproducing Kernels

Authors: Heinrich Begehr, Saburou Saitoh
Comments: 8 Pages.

In this note, we wrote the preface for the first volume of the International Journal of Reproducing Kernels (The Roman Science Publications and Distributions (RSPD): https://romanpub.com/ijrk.php). Incidentally, this year is one century since the origin of reproducing kernels at Berlin. For some detailed information of the origin and some global situation of the theory of reproducing kernels with the content of the first volume are introduced.
Category: Functions and Analysis