Find the generating functions of the sequences of Chebyshev polynomials of the first and second kind: \[F_T(x,z) = \sum_{n=0}^{\infty}T_n(x)z^n;\quad F_U(x,z) = \sum_{n=0}^{\infty}U_n(X)z^n.\]
Definitions of Chebyshev polynomials can be found in the handbook.