Chenge weight function in shifted orthogonality We know that in Chebyshev orthogonal polynomial the weight function is $$\frac{1}{\sqrt{1-x^2}}$$ in interval $[-1,1]$. Do in shifted chebyshev orthogonal as example for interval $[0,1]$ the weight function changed?

What you need is a scaling function $K(x)$ so that
$$
\left< T_n, T_m \right>
   = \int_0^1 T_n(x) T_m(x) K(x) dx
   = 0 \quad \text{for } n \ne m,
$$
which is the orthogonality criterion.
In the standard case, picking $$K(x) = \frac{1}{\sqrt{1-x^2}},$$ guarantees
$$
\left< T_n, T_m \right>
   = \int_{-1}^1 T_n(x) T_m(x) K(x) dx
   = 0 \quad \text{for } n \ne m
$$
