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Abstract

The Hardy–Hilbert integral inequality has been the subject of extensive study in recent decades. In this article, we present a two-parameter exponential generalization of this inequality. The associated constant factor involves the upper incomplete gamma function. Interestingly, it can also be expressed in terms of the classical error function. Through precise analysis, we prove the optimality of this constant. We then derive several integral inequalities of various types, some involving primitive functions, while others incorporating auxiliary functions.