Geodesic
On some rational functions which are analogues of Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 106-120

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In this paper, rational functions, which are analogues of Chebyshev polynomials of the second, third and fourth kind, are considered. These rational functions are extremal in Bernstein type inequalities with corresponding weights. Orthogonalization of mentioned functions also is presented. 
@article{ZNSL_2014_429_a8,
     author = {S. I. Kalmykov},
     title = {On some rational functions which are analogues of {Chebyshev} polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {106--120},
     publisher = {mathdoc},
     volume = {429},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a8/}
}
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S. I. Kalmykov. On some rational functions which are analogues of Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 106-120. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a8/