In this paper, we introduce generalized formulae for well-known polynomials such as Chebyshev polynomials. We define \((\beta ,\gamma )\) -Chebyshev polynomial, \((\beta ,\gamma )\) -pseudo-Chebyshev wavelet approximation and \((\beta ,\gamma )\) -pseudo Chebyshev wavelet coapproximation. We show if for \(f \in L^2([-1,1])\) is a uniformly bounded function and \(f (t) =\sum _{n=0}^{2^k}\sum _{m=0}^{\infty }t_{n,m}\Psi _{n,m}^{\beta ,\gamma }(t)\) be expanded in terms of \((\beta ,\gamma )\) -Chebyshev wavelets ( \((\beta ,\gamma )\) -pseudo Chebyshev wavelets). Then wavelets Chebyshev approximation (wavelets Chebyshev coapproximation) exist.
