Why Do Common Functions Use Asymptotic Expansion Series?

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Asymptotic expansion series are preferred for functions like the Gamma function, Error function, and Riemann Zeta function due to their ability to provide approximations that are valid in specific limits, particularly for large arguments. These series offer simpler calculations and insights into the behavior of functions compared to other expansion methods. The choice of asymptotic expansions often stems from their effectiveness in capturing the dominant behavior of functions in asymptotic analysis. Understanding why these functions utilize asymptotic expansions can enhance comprehension of their mathematical properties and applications. Exploring the detailed reasoning behind these choices is crucial for a deeper grasp of asymptotic series in mathematical techniques.
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Hello and good day. I am searching for Asymptotic Series for my Mathematical Technique mini project. I'm doing Asymptotic Expansion Series and the examples of it. I search on the internet and I found few examples of it such as Gamma Function, Error Function, Riemann Zeta Function, Exponential Integral and Multiple Integral.
But my lecturer have giving me some twist, he asked me to find why all the examples that I found, choose Asymptotic Expansion Series instead of other expension series.

Thanks.
 
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I don't see why e.g. the Gamma function is an asymptotic expansion, so a more detailed explanation would have been helpful. However, the link also discusses your question in section 2.2.2
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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