1. Introduction. Let b, d, , n and y be positive integers such that gcd(n, d) = 1 and > 2 is a prime number. Let k ≥ 2, t ≥ 2 and r ∈ {0, 1} be integers satisfying t = k − r. Thus k ≥ 2 if r = 0 and k ≥ 3 if r = 1. Let d 1 < . . . < d t be integers in the interval [0, k). We write

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

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