DOI: 10.3390/axioms15080577 ISSN: 2075-1680
Inequalities for ζ(s) − ψ(1 − s) Related to a Conjecture of Henry
Liwen GaoIn this paper, we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating ζ(s)−ψ(1−s) as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary limits of the derivative, expressed in terms of π, log(2π) and Stieltjes constants. These results lead to new inequalities for ζ(s)−ψ(1−s) and shed further light on the conjecture.