Functions and Analysis

1811 Submissions

[7] viXra:1811.0510 [pdf] submitted on 2018-11-29 10:08:17

Confirmation of the Logic in the Definition of the K-Triangular Set Function

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the logic of the definition of the k-triangular function in set theory and find it tautologous, hence confirming it as a theorem.
Category: Functions and Analysis

[6] viXra:1811.0496 [pdf] submitted on 2018-11-28 06:20:10

Dieudonné-Type Theorems for Lattice Group-Valued K-Triangular Set Functions

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 19 Pages.

Some versions of Dieudonne-type convergence and uniform boundedness theorems are proved, for k-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case.
Category: Functions and Analysis

[5] viXra:1811.0330 [pdf] submitted on 2018-11-22 02:48:05

The Gamma Function

Authors: James Bonnar
Comments: 161 Pages.

This book is dedicated to the subject of the Gamma function and related topics. The Gamma Function is primarily intended for advanced undergraduates in science and mathematics. It is concise yet thorough and covers each of the most important aspects of the Gamma function. The Gamma function has important applications in probability theory, combinatorics and most, if not all, areas of physics. A large number of proofs and derivations of theorems and identities are covered in the book including: Analytic continuation of the factorials, properties via complex analysis, Holder's theorem, the Bohr-Mullerup theorem, the Beta function, Wallis's integrals, Wallis's product, product & reflection formulas, half-integer values, digamma and polygamma functions, series expansions, Euler-Mascheroni integrals, duplication & multiplication formulas, the Gamma and zeta function relationships, Hankel's contour integral representation, Stirling's formula, the Weierstrass factor theorem and the Mittag-Leffler theorem.
Category: Functions and Analysis

[4] viXra:1811.0281 [pdf] submitted on 2018-11-19 04:01:17

Arithmetic of Analysis II

Authors: Fayowole David Ayadi
Comments: 2 Pages.

This work is an alternate method of evaluating absolute (modulus) value.
Category: Functions and Analysis

[3] viXra:1811.0244 [pdf] submitted on 2018-11-15 06:38:41

Remark on the paper of Zheng Jie Sun and Ling Zhu

Authors: Yogesh J. Bagul
Comments: 4 Pages. In this paper , a mathematical mistake is discovered and another simple proof of the theorem is proposed.

In this short review note we show that the new proof of theorem 1.1 given by Zheng Jie Sun and Ling Zhu in the paper Simple proofs of the Cusa-Huygens-type and Becker-Stark-type inequalities is logically incorrect and present another simple proof of the same.
Category: Functions and Analysis

[2] viXra:1811.0222 [pdf] replaced on 2018-12-10 09:38:19

Real Numbers in the Neighborhood of Infinity

Authors: Jonathan W. Tooker
Comments: 12 Pages.

We demonstrate the existence of a broad class of real numbers which are not elements of any number field: those in the neighborhood of infinity. After considering the reals and the affinely extended reals we prove that numbers in the neighborhood of infinity are ordinary real numbers. As an application in complex analysis, we show that the Riemann zeta function has infinitely many non-trivial zeros off the critical line in the neighborhood of infinity.
Category: Functions and Analysis

[1] viXra:1811.0180 [pdf] submitted on 2018-11-11 12:59:10

Negation of the Riemann Hypothesis

Authors: Jonathan W. Tooker
Comments: 4 Pages. arXiv - submit/2464257 removed: " The moderators have rejected your submission as "unrefereeable": your article does not contain sufficient original or substantive scholarly research."

We show that the Riemann zeta function has infinitely many non-trivial zeros off the critical line.
Category: Functions and Analysis