Expand a function in terms of Legendre polynomials

[Logarythmic]

Problem:
Suppose we wish to expand a function defined on the interval (a,b) in terms of Legendre polynomials. Show that the transformation u = (2x-a-b)/(b-a) maps the function onto the interval (-1,1).

How do I even start working with this? I haven't got a clue...

 

[quasar987]

I do not speak english in everyday life, and so the words "maps the function onto the interval (-1,1)" seems confusing to me. I would normally interpret them as "u is such that u\circ f:(a,b)-->(-1,1)". But that does not seem to make sense, since we do not know the form of f. What does make sense, is to understand it as "u is such that f\circ u:(a,b)-->R is the same as f:(-1,1)-->R". In other words, you need to show that f\circ u is a restriction of f. But that is easy, you only need to show that u is onto from (a,b) to (-1,1).

 

[Logarythmic]

Ok, I'm really not good at linear algebra so I think I'll jump this problem. ;)