AbstractLet ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-function. Let q be a positive integer greater than 1 and γ denote Euler's constant. We show that all the numbersψ(a/q)+γ,(a,q)=1,1⩽a⩽q, are transcendental. We also prove that at most one of the numbersγ,ψ(a/q),(a,q)=1,1⩽a⩽q, is algebraic.