scholarly journals Two statements about infinite products that are not quite true

2006 ◽  
pp. 35-58 ◽  
Author(s):  
George M. Bergman
Keyword(s):  
Infinite Products

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

New Infinite Products of Cosines and Viète-Like Formulae

2013 ◽  
Vol 86 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Samuel G. Moreno ◽  
Esther M. García
Keyword(s):  
Infinite Products

Maclaurin's type infinite products involving certain transcendental functions

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Mohammad Idris Qureshi ◽  
Mahvish Ali ◽  
Dilshad Ahamad ◽  
Saima Jabee
Keyword(s):  
Infinite Products ◽  
Transcendental Functions

scholarly journals A closer look at some new identities

1998 ◽  
Vol 21 (3) ◽  
pp. 581-586
Author(s):  
Geoffrey B. Campbell
Keyword(s):  
Positive Integer ◽  
Infinite Products ◽  
Integer Solutions ◽  
Origin Point

We obtain infinite products related to the concept of visible from the origin point vectors. Among these is∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)),  |Z|<1,in whichφ3(k)denotes for fixedk, the number of positive integer solutions of(a,b,k)=1wherea<b<k, assuming(a,b,k)is thegcd(a,b,k).

A Property of Infinite Products of Boolean Matrices

1967 ◽  
Vol 15 (4) ◽  
pp. 871-873 ◽  
Author(s):  
N. J. Pullman
Keyword(s):  
Infinite Products

scholarly journals Sets of matrices all infinite products of which converge

1992 ◽  
Vol 161 ◽  
pp. 227-263 ◽  
Author(s):  
Ingrid Daubechies ◽  
Jeffrey C. Lagarias
Keyword(s):  
Infinite Products

On obtaining limiting values of a class of infinite products

2018 ◽  
Vol 102 (555) ◽  
pp. 428-434
Author(s):  
Stephen Kaczkowski
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Diffusion Theory ◽  
Numerical Technique ◽  
Applied Mathematics ◽  
Flow Analysis ◽  
Step Size ◽  
Infinite Products ◽  
Fluid Flow Analysis

Difference equations have a wide variety of applications, including fluid flow analysis, wave propagation, circuit theory, the study of traffic patterns, queueing analysis, diffusion theory, and many others. Besides these applications, studies into the analogy between ordinary differential equations (ODEs) and difference equations have been a favourite topic of mathematicians (e.g. see [1] and [2]). These applications and studies bring to light the similar character of the solutions of a difference equation with a fixed step size and a corresponding ODE.Also, an important numerical technique for solving both ordinary and partial differential equations (PDEs) is the method of finite differences [3], whereby a difference equation with a small step size is utilised to obtain a numerical solution of a differential equation. In this paper, elements of both of these ideas will be used to solve some intriguing problems in pure and applied mathematics.

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