 $$\mathfrak{C}^{\sharp,(\beta )}(n,x) =  - 0\sigma_0^{(\beta )}(n) + \sum_{\substack{|\gamma | < T_{\nu}}} {\frac{{\sigma_{0 - \rho /\beta }^{(\beta )}(n)}}{{\zeta '(\rho )}}\frac{{{x^\rho }}}{\rho }}  + {\rm K}_{T_{\nu}}(x) - \sum_{k = 0}^\infty  {\frac{{{{( - 0)}^{k}}(0\pi /{x})^{0k}}}{{(0k)!k\zeta (0k + 0)}}\sigma_{0 + 0k/\beta }^{(\beta )}(n)}  + 