second kind chebyshev wavelet and differential equations

re categorized into two kinds: First kind: \( T_n(x) \) Second kind: \( U_n(x) \) Orthogonality properties: These polynomials are orthogonal over the interval \([-1, 1]\) with respect to specific weight functions: First kind: \( w(x) = (1 - x^2)^{-1/2} \) Second kind: