How to Reduce a Function to a Hypergeometric Using a Change of Variables?

Thread starter blocnt
Start date Oct 29, 2013
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Function Hypergeometric Hypergeometric function

In summary, a hypergeometric function is a solution to a specific type of differential equation and is used in various fields such as statistics, probability, and quantum mechanics. It is different from other functions in that it has an infinite number of terms and a unique power series expansion. It has applications in probability, special functions, quantum mechanics, and more. Some main properties include power series expansions, recurrence relations, and integral representations. Common examples include the Gaussian hypergeometric function, the confluent hypergeometric function, and the hypergeometric series.

Oct 29, 2013

blocnt

I'm having difficulty in solving an exercise.

http://imageshack.us/a/img542/484/765z.jpg

They ask to reduce it to
http://imageshack.us/a/img203/3986/lwqb.jpg
making the change of variables x=r^2/(r^2+1)

and then to reduce it to a hypergeometric , using http://img41.imageshack.us/img41/4479/syz6.jpg

Thanks in advance

Last edited by a moderator: May 6, 2017

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Oct 31, 2013

MathematicalPhysicist

Gold Member

HW question, inappropriate.

1. What is a hypergeometric function?

A hypergeometric function is a mathematical function that is defined as a solution to a certain type of differential equation. It is a special type of function that is used in many areas of mathematics and physics, including statistics, probability, and quantum mechanics.

2. How is a hypergeometric function different from other types of functions?

Unlike most other functions that have a finite number of terms, a hypergeometric function has an infinite number of terms. It also has a unique power series expansion that is used to define it. Additionally, a hypergeometric function can be expressed as a ratio of two other functions.

3. What are the applications of hypergeometric functions?

Hypergeometric functions have a wide range of applications in various fields of mathematics and physics. They are used to solve problems related to probability and statistics, as well as in the study of special functions, such as the Bessel functions and the Gamma function. They are also used in fields such as quantum mechanics, fluid dynamics, and number theory.

4. What are the main properties of hypergeometric functions?

Some of the main properties of hypergeometric functions include their power series expansions, their recurrence relations, and their integral representations. They also have certain symmetries and transformations that can be used to simplify their calculations. Additionally, hypergeometric functions have specific conditions for their convergence and divergence.

5. What are some common examples of hypergeometric functions?

Some commonly used hypergeometric functions include the Gaussian hypergeometric function, the confluent hypergeometric function, and the hypergeometric series. Other examples include the Appell hypergeometric function, the Lauricella hypergeometric function, and the Meijer G-function. These functions have various applications in different branches of mathematics and physics.