- #1
Grothard
- 29
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If f(z) and g(z) share all the same poles, is f(z)-g(z) pole-free? I feel like this would be true, but I can't really come up with a proof for it.
The difference of two functions sharing the same poles pole-free is a mathematical concept where two functions have the same poles (points where the function is undefined) and the difference between them does not have any additional poles.
The difference of two functions sharing the same poles pole-free is calculated by subtracting one function from the other. This means that the value of the difference at any given point is equal to the difference between the values of the two functions at that point.
No, the difference of two functions sharing the same poles pole-free cannot have any poles. This is because the poles of the two functions cancel each other out when subtracted, resulting in a function that is pole-free.
Two functions sharing the same poles pole-free are important in the study of complex analysis. They can help simplify calculations and provide insights into the behavior of functions with poles.
The concept of difference of two functions sharing the same poles pole-free can be applied in various fields such as physics, engineering, and economics. It can be used to model complex systems and analyze their behavior, as well as to solve various mathematical problems involving functions with poles.