  By the method of weight coefficients, techniques of real analysis and
Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality
related to the kernel of the hyperbolic cosecant function with the best
possible constant factor expressed in terms of the extended Riemann-zeta
function is proved. The more accurate equivalent forms, the operator
expressions with the norm, the reverses and some particular cases are also
considered.
