Rewriting Legendre's Equation for Orthogonality

  • Thread starter popo902
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In summary, the conversation is about orthogonality of Legendre's polynomials and a rewritten form of Legendre's equation. The person is having trouble understanding how to get to the rewritten form and asks for an explanation. Another person provides a simple solution using the product rule and the conversation ends with the person thanking for the explanation.
  • #1
popo902
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Homework Statement



i was reading on orthogonality of Legenedre's polynomials
and this equation came up

http://www.hit.ac.il/ac/files/shk_b/Differential.Equations/Orthogonality_of_Legendre_polynomials_files/img39.gif

It's a rewritten form of Legendre's equation, but i can't see how to get there
can someone explain how to get there from the original equation?

Homework Equations



Original

http://mathworld.wolfram.com/images/equations/LegendreDifferentialEquation/NumberedEquation1.gif

The Attempt at a Solution

 
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  • #2
It's quite simple:

[tex]
\frac{d}{dx}((1-x^{2})y')=(1-x^{2})y'' -2xy'
[/tex]

From the product rule using 1-x^2 and y'
 
  • #3
i can't believe i didn't see that
haha thank you once again
 

FAQ: Rewriting Legendre's Equation for Orthogonality

What does it mean to rewrite an equation?

Rewriting an equation means to rearrange the terms and/or variables in an equation to make it more easily solvable or to solve for a different variable.

Why would you need to rewrite an equation?

There are several reasons for rewriting an equation, such as simplifying it, solving for a different variable, or making it easier to understand and work with.

How do you rewrite an equation?

To rewrite an equation, you can use various algebraic techniques such as distributing, combining like terms, factoring, and isolating variables. The specific method used will depend on the equation and what you are trying to achieve by rewriting it.

Can you change the meaning of an equation by rewriting it?

Yes, rewriting an equation can change its meaning if the rearranged terms and variables result in a different solution or a different variable being solved for. However, the underlying mathematical relationship between the values will remain the same.

Are there any rules or guidelines for rewriting an equation?

While there are no strict rules for rewriting an equation, it is important to maintain the equality of both sides of the equation and to follow the standard conventions of algebra. It is also helpful to clearly document each step taken to avoid errors and make it easier for others to follow the process.

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