Yosida functions and Picard values of integral functions and their derivatives

In this paper we improve and generalise a result of J. Clunie by proving that if f(z) is a transcendental integral function with only zeros of order at least k + 1, then f((k))(z) assumes every finite non-zero complex value infinitely often. Also, the related criterion for normality of a family of holomorphic functions is given, and the value distribution of f(2) + af((k)) is discussed.