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On obtaining limiting values of a class of infinite products

Published online by Cambridge University Press:  17 October 2018

Stephen Kaczkowski
Stephen Kaczkowski*
Affiliation:
South Carolina Governor's School, 401 Railroad Avenue, Hartsville, SC 29550USA e-mail: kaczkowski@gssm.k12.sc.us
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Extract

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.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 428 - 434
Copyright
Copyright © Mathematical Association 2018 

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References

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