Legendre Funcs: Homework & Equations Explained

In summary, The conversation is about understanding Legendre functions and their recursion, as well as creating a program to compute and plot normalized legendre functions. The equations and subscripted n/m notation are causing confusion for the speaker. They believe they need to create a recursive function to solve the problem.
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Homework Statement



Hi everyone, I am having issues understanding how Legendre functions work especially the recursion and what the subscripts mean in general. I am attempting to make a program to compute the legendre functions Pnm(cos(theta)) and the normalized version and then verifying it by plotting 4 normalized legendre functions.

I don't understand what to do with these equations to get to what I'm attempting to do they just confuse me to no end.

Homework Equations



http://img14.imageshack.us/img14/5976/legendre.png

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I'm pretty sure I have to make a function to start with the original equation and then recursively go down. What do the subscripted n/m mean I'm confused on that as well xD
 
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1. What are Legendre Functions?

Legendre Functions are a type of special mathematical functions that are used to solve problems in various fields of science and engineering. They are named after the French mathematician Adrien-Marie Legendre, who first described them in the late 18th century.

2. What is the purpose of studying Legendre Functions?

Studying Legendre Functions is important because they have many applications in physics, engineering, and mathematics. They are used to solve differential equations, describe the motion of celestial bodies, and model physical phenomena such as heat transfer and electricity.

3. How are Legendre Functions defined?

Legendre Functions are defined as solutions to the Legendre differential equation, which is a second-order linear differential equation. They are typically denoted by Pn(x) or Qn(x) where n is the degree of the function and x is the variable.

4. What are the key properties of Legendre Functions?

Legendre Functions have many important properties, including orthogonality, recursion, and generating functions. These properties make them useful for solving a wide range of problems in mathematics and physics.

5. How can I use Legendre Functions in my research or work?

If you are working in a field that involves solving differential equations or modeling physical phenomena, you may encounter problems where Legendre Functions can be applied. In such cases, you can use the equations and techniques explained in this homework to solve the problem and analyze the results.

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