An extension of the Chebyshev polynomials

We consider a generalization of the Chebyshev polynomials of the second kind. These polynomials can be expressed as transformed Chebyshev polynomials of a complex variable. The idea of this generalization comes from an extension of typically real functions, where as the kernel function appears the q-Koebe functions proposed by Gasper (SIAM J. Math. Anal. 20 (1989) 1019), which play the role of generating function.