On a moment problem associated with Chebyshev polynomials

Given a sequence {μn}n=0∞ of real numbers, we find necessary and sufficient conditions for the existence and uniqueness of a distribution function ϕϕ on (1,∞)(1,∞), such thatμn=∫1∞Tn(x)dϕ(x),n=0,1,2,….Here Tn(x)Tn(x) are the Chebyshev polynomials of the first kind.