Complete monotonicity of a function involving the p-psi function and alternative proofs - Krasniqi, Valmir; Qi, Feng (Global Journal of Mathematical Analysis, 2014)
In the paper, the authors prove that the function x^α[pxx+p+1-ψ_p(x)] is completely monotonic on (0,∞) if and only if α 1, where pN and ψ_p(x) is the p-analogue of the classical psi function ψ(x).Keywords: completely monotonic function; necessary and sufficient condition; p-gamma function; p-psi function; Inequality MSC: Primary 33D05; Secondary 26A48, 33B15, 33E50