Defining Legendre polynomials in (1,2)

[confused_engineer]

Hello everyone.

The Legendre polynomials are defined between (-1 and 1) as 1, x, ½*(3x²-1), ½*(5x³-3x)...

My question is how can I switch the domain to (1, 2) and how can I calculate the new polynomials.

I need them to construct an estimation of a random uniform variable by chaos polynomials between 1 and 2

Thanks

 

[Stephen Tashi]

Change coordinates to obtain polynomials in a new variable w.
Let w = Ax + B and choose A and B so that w= 1 at x = -1 and w =2 at x = 1.

 

[confused_engineer]

Change coordinates to obtain polynomials in a new variable w.
Let w = Ax + B and choose A and B so that w= 1 at x = -1 and w =2 at x = 1.

Indeed this checks out with the numerical model estimation.
Thanks.