TL;DR
This paper introduces a novel 'star-integral' that replaces summation with multiplication, explores its properties, and relates it to a new 'star-derivative', offering a different perspective on integral calculus.
Contribution
It defines the 'star-integral' and 'star-derivative', establishing their properties and connections to standard calculus, providing a new mathematical framework.
Findings
Star-integral can be expressed in terms of the standard integral.
Star-derivative is related to the star-integral through a specific relationship.
The properties of star-integral differ from but are analogous to standard integrals.
Abstract
In this paper, we discuss a similar functional to that of a standard integral. The main difference is in its definition: instead of taking a sum, we are taking a product. It turns out this new "star-integral" may be written in terms of the standard integral but it has many different (and similar) interesting properties compared to the regular integral. Further, we define a "star-derivative" and discuss its relationship to the "star-integral".
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Taxonomy
TopicsAdvanced Mathematical Theories · Mathematics and Applications