In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...

The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants $\{\lambda _{k}\}_{k=1}^{\infty}$ that are certain logarithmic derivatives of the Riemann xi function ...