Square-free Integers and Infinite products
Ramesh Kumar Muthumalai
TL;DR
This paper explores properties of square-free integers, derives infinite products involving them, and introduces a method to convert series into infinite products, with applications to trigonometric functions and factorials.
Contribution
It presents a novel method for transforming power and trigonometric series into infinite products, utilizing properties of square-free integers.
Findings
Derived new infinite product formulas involving square-free integers
Developed a method to convert series into infinite products
Applied the method to elementary trigonometric functions and factorials
Abstract
We study few properties of square-free integers in certain equations. Using this property, we derive some infinite products in powers of square free numbers. Also, we present a method, to convert power series and trigonometric series to infinte products. Infinite products of few elementary trigonometric functions and factorials for large numbers are shown as examples.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Numerical Methods and Algorithms · Polynomial and algebraic computation