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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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Q: Third- and fourth-kind polynomials CHEBYSHEV
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