Help With Gamma Function Homework

In summary, The equation I (2n,m) = Integral cos^(2n)O sin^(m)O cosO dO, with limits 0 to 2pi and O = theta, can be solved using integration by parts to establish the relationship I 2n,m = 2n/ m+1 (I2n-2, m+2). This problem is related to the Gamma function in the instructor's notes and an example of a similar problem could be helpful in finding the solution.
  • #1
Integral8850
15
0

Homework Statement



I (2n,m) = Integral cos^(2n)O sin^(m)O cosO dO
limits are 0 to 2pi and O = theta

0.4/3 = 0.1333

show that I 2n,m = 2n/ m+1 (I2n-2, m+2)

Homework Equations


I really have no idea how to work with this problem. It is under Gamma function of the instructors notes. I have searched for an hour for an example similar to this problem. If anyone could point me in the right direction or a direction I would be greatful!

Thanks


The Attempt at a Solution

 
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  • #2
Usually to establish this kind of relationship, you can use integration by parts. Have you tried that?
 

FAQ: Help With Gamma Function Homework

What is the gamma function?

The gamma function is a mathematical function that is used to extend the factorial function to non-integer numbers. It is denoted by the symbol Γ and has many applications in mathematics and physics.

How do I calculate the value of the gamma function?

The value of the gamma function can be calculated using various mathematical formulas or by using a computer program or calculator. The most commonly used method is the Lanczos approximation, which is a series expansion that gives accurate results for most values of the gamma function.

What are the properties of the gamma function?

Some of the important properties of the gamma function include: it is defined for all complex numbers except for negative integers, it is an entire function, it satisfies the functional equation Γ(z+1) = zΓ(z), and it has poles at the negative integers. Additionally, it has connections to many other mathematical functions such as the beta function and the hypergeometric function.

What are the applications of the gamma function?

The gamma function has many applications in mathematics, physics, and engineering. Some of its uses include: evaluating integrals, solving differential equations, calculating probabilities in statistics, and in the field of number theory, among others. It also has applications in areas such as quantum mechanics, particle physics, and signal processing.

How can I get help with my gamma function homework?

If you need assistance with your gamma function homework, there are several resources available to you. You can seek help from your teacher or professor, attend tutoring sessions, or join a study group. There are also many online resources such as videos, tutorials, and forums where you can find help and guidance for your homework. Additionally, you can hire a private tutor or seek help from a professional math tutor.

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