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Yes, there are Chebyshev polynomials of the third and fourth kind, not just the first and second.
The third kind is often denoted Vn (x) and it is
Vn(x)=(1-x)1/2 (1+x)-1/2 and the domain is (-1,1)
Chebychev polynomials of the fourth kind are deonted
wn(x)=(1-x)-1/2 (1+x)1/2
As with other Chebychev polynomials, they are orthogonal.
They are both special cases of Jacobi polynomials.
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