Expressing the difference of two Hurwitz zeta functions by a linear combination of the Gauss hypergeometric functions

Feng Qi

In the paper, the author expresses the difference $2^m\left[\zeta \right(-m,\frac{1+x}{2})-\zeta (-m,\frac{2+x}{2}\left)\right]$ in terms of a linear combination of the function $Γ(m…