Asymptotics Book Recommendation

Aside from Bender and Orszag, another good resource is "Asymptotic Expansions" by Olver.In summary, the conversation is discussing recommendations for expository books or articles that contain derivations of asymptotic expansions of special functions. Abramowitz and Stegun's book is mentioned as containing the results but not the derivations, while "Advanced Mathematical Methods for Scientists and Engineers" by Bender and Orszag is recommended as having a nice presentation. Another suggested resource is "Asymptotic Expansions" by Olver.
  • #1
sheaf
220
7
Can anyone recommend an expository book or article containing some of the derivations of the asymptotic expansions of special functions? Many of the "lookup" type books such as Abramovitz and Stegun contain the results but not the derivation of the results.
 
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  • #2
A nice presentation is in "Advanced Mathematical Methods for Scientists and Engineers" by Bender and Orszag.

jason
 
  • #3
OK thanks very much - I'll take a look at that one !
 
  • #4
sheaf said:
Can anyone recommend an expository book or article containing some of the derivations of the asymptotic expansions of special functions? Many of the "lookup" type books such as Abramovitz and Stegun contain the results but not the derivation of the results.

Abramowitz and Stegun has little references beside each entry, doesn't it?
 
  • #5


Asymptotic expansions of special functions are an important tool in mathematical analysis and have various applications in physics, engineering, and other fields. I would recommend the book "Asymptotic Analysis" by Tomasz K. Korzeniowski for a comprehensive and accessible introduction to this topic. This book covers the derivation of asymptotic expansions for a wide range of special functions and provides clear explanations and examples to aid understanding. Additionally, "Asymptotic Expansions" by N.G. de Bruijn is another excellent resource for learning about the mathematical foundations and applications of asymptotic expansions. Both of these books provide a solid foundation for understanding the derivations of asymptotic expansions and their importance in scientific research.
 

1. What is asymptotics?

Asymptotics is a branch of mathematics that deals with the behavior of mathematical functions as their input values approach a particular value, such as infinity or zero. It is often used to analyze the performance of algorithms and study the properties of functions.

2. Why is asymptotics important in book recommendations?

Asymptotics can be used to analyze the growth rate of data, such as the number of books in a database or the number of users. This analysis can help determine the most efficient algorithms for recommending books and improve the overall performance of the recommendation system.

3. How is asymptotics applied in book recommendation systems?

Asymptotics is often used in the design and analysis of algorithms for book recommendations. It can help determine the time and space complexity of different algorithms and guide the selection of the most efficient approach for a given dataset and use case.

4. What are some limitations of using asymptotics in book recommendations?

While asymptotics can provide valuable insights into the performance of algorithms, it does not take into account real-world factors such as user preferences and behavior. As a result, the effectiveness of recommendation systems based solely on asymptotic analysis may be limited.

5. Are there any alternative methods to asymptotics for book recommendations?

Yes, there are alternative methods such as machine learning and collaborative filtering that can be used in book recommendation systems. These methods take into account real-world data and user behavior to make personalized recommendations, which can often be more effective than purely asymptotic-based approaches.

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