]> $${\psi }^{\left(n\right)}\left(x\right)={\left(-1\right)}^{n+1}n!\sum _{k=0}^{\infty }\frac{1}{{\left(k+x\right)}^{n+1}}=\frac{{\partial }^n\psi \left(x\right)}{{\partial }^{n}x}$$