On a class of Hilbert-type inequalities in the whole plane related to exponent function - You, Minghui (Journal of inequalities and applications, 2021)
By introducing a kernel involving an exponent function with multiple parameters, we establish a new Hilbert-type inequality and its equivalent Hardy form. We also prove that the constant factors of the obtained inequalities are the best possible. Furthermore, by introducing the Bernoulli number, Euler number, and the partial fraction expansion of cotangent function and cosecant function, we get some special and interesting cases of the newly obtained inequality.