Chebyshev nodes

Chebyshev nodes are a useful choice for interpolation.

For n+1 nodes on the interval [-1, 1], the Chebyshev nodes would be defined by

$x_{i}=cos\left({\frac {2i+1}{2n+2}}\pi \right)$

where

$0\leq i\leq n$

For an arbitrary interval [a, b], a linear transformation can be used to get

$x_{i}={\frac {1}{2}}(a+b)+{\frac {1}{2}}(b-a)cos\left({\frac {2i+1}{2n+2}}\pi \right)$