A good reference book on hypergeoemetric series?

In summary, a hypergeometric series is a mathematical series with three parameters and involves the falling factorial function. It differs from other series in its convergence conditions and has various applications in physics, statistics, and engineering. A good reference book on the subject should have a clear explanation, examples, and exercises, be well-organized, and recommended by experts in the field. While a strong mathematical background can be helpful, it is not necessary to understand hypergeometric series, but a basic understanding of algebra and calculus is necessary.
  • #1
Arian.D
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I'm looking for an elementary book that has no prerequisites other than calculus, differential equations and elementary number theory about hypergeometric series. If it has good exercises in the end of each chapter, that would be great. Any suggestions would be appreciated.
 
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  • #2
No one knows? Really?
Am I the only person out there that is interested in hyper geometric series?
 

1. What is a hypergeometric series?

A hypergeometric series is a mathematical series that involves three parameters: a, b, and c. It is given by the formula ∑(n=0 to ∞) [(a)_n(b)_n/(c)_n] x^n, where (a)_n is the falling factorial of a and n, (b)_n is the falling factorial of b and n, and (c)_n is the falling factorial of c and n.

2. How is a hypergeometric series different from other mathematical series?

A hypergeometric series differs from other mathematical series in that it has three parameters and involves the falling factorial function. It also has specific conditions for convergence, such as the ratio of consecutive terms approaching a finite limit.

3. What are some applications of hypergeometric series in science?

Hypergeometric series have various applications in fields such as physics, statistics, and engineering. In physics, they are used to model physical systems with discrete energy levels. In statistics, they are used in probability distributions and in solving problems related to sampling without replacement. In engineering, they are used in circuit analysis and signal processing.

4. What should I look for in a good reference book on hypergeometric series?

A good reference book on hypergeometric series should have a clear explanation of the concept and its various applications. It should also provide examples and exercises for practice. The book should be well-organized and have a comprehensive index and references for further reading. Additionally, the author should have expertise in the subject and the book should be recommended by other experts in the field.

5. Is it necessary to have a strong mathematical background to understand hypergeometric series?

While a strong mathematical background can be helpful, it is not necessary to have a deep understanding of advanced mathematics to grasp the concept of hypergeometric series. Many introductory books on the subject assume only a basic knowledge of algebra and calculus. However, a good understanding of mathematical concepts such as series, limits, and factorials is necessary to fully grasp the concept and its applications.

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