On a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of exponential function

By applying the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of exponential function with the best possible constant factor expressed by the gamma function is given. The more accurate equivalent forms, the operator expressions with the norm, the reverses, and some particular cases are considered.