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By the method of weight coefficients, techniques of real analysis andHermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the bestpossible constant factor expressed in terms of the extended Riemann-zetafunction is proved. The more accurate equivalent forms, the operatorexpressions with the norm, the reverses and some particular cases are alsoconsidered.

A More Accurate Half-Discrete Hardy-Hilbert-Type Inequality with the Best Possible Constant Factor Related to the Extended Riemann-Zeta Function