It is well-known that the Chebyshev polynomials of the first kind satisfy the recurrence relation $$ \begin{cases} T_{n}(x)=2xT_{n-1}(x)-T_{n-2}(x) \qquad n \geq 2 \\ T_{0}(x)=1, \ \ T_{1}(x)=x \\ \end{cases} $$

The perturbed Chebyshev polynomials are defined by the recurrence $$f_0(x)=b,\ \ f_1(x)=x−c,\ \ f_{n+1}(x)=(x−d)f_n(x)−af_{n−1}(x),\ n\geq1, $$ where $a,b,c,d\in \mathbb R$ and $a>0$. These polynomials generalize the Chebyshev polynomials, which are obtained by setting $a=1/4$, $c=d=0$ and $b\in\{1,2\}$. See, for example:

Stoll, Thomas. "Decomposition of perturbed Chebyshev polynomials." Journal of Computational and Applied Mathematics 214.2 (2008): 356-370.

Let us consider the sequence $\{T_n\}_{n\in\mathbb N}$. Perturb this sequence could mean also consider $\{T_{\alpha_n}\}_{n\in\mathbb N}$ with $\alpha_n$ is a sequence of real numbers. I wonder if a similar sequence of Chebyshev polynomials is known, and if it is used in some applications. I thought this question by reading some articles on Non-harmonic Fourier series, where $\{e^{i n t}\}_{n\in\mathbb N}$ is replaced by $\{e^{i \alpha_n t}\}_{n\in\mathbb N}$.

Thanks in advance.