A Hilbert-type inequality related to the higher derivative of cotangent function
By introducing multiple parameters,and using partial fraction expansion of Cotangent function,a new Hilbert-type inequality defined in the whole plane with the constant factor related to the higher derivative of cotangent function is established.Also,the equivalent form of the inequality is considered.Furthermore,assigning different values to the parameters,some special Hilbert-type inequalities defined in the whole plane are obtained.
Hilbert inequalitycotangent functionpartial fraction expansionHurwitz Zeta functionGamma function
万方数据
维普
