In this paper, by constructing a new non-homogeneous kernel of mixed hyperbolic functions, we establish a new Hilbert-type integral inequality with the best constant factor. We also consider the equivalent form of the obtained inequality. Moreover, by using the rational fraction expansion of cotangent function and cosecant function, some special Hilbert's type inequalities with the constant factors related to the higher derivatives of cotangent function and cosecant function are presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.