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For the higher order derivative(with respect to the first variable) ofHurwitz zeta function,we discuss as a function of the second variable,thelocation and the nature of its singularities and obtain the formulae for itsderivative and primitive and also discuss its Riemann integrability on the unitinterval and on the interval[1,infinity).We also evaluate certain integrals onthe unit interval involving these functions.

The alpha-calculus-cum-alpha-analysis of r-th order derivative of zeta(s,alpha)