Derivatives of Multiple $$\log \Gamma $$ -Type Functions

Abstract In this chapter, we discuss the higher order differentiability properties of Σ g when lies in $$\mathcal {C}^r\cap \mathcal {D}^p\cap {K}^{\max \{p,r\}}$$ C r ∩ D p K max { , } for any $$p,r\in \mathbb {N}$$ ∈ ℕ . particular, show fundamental fact that also {C}^r$$ and sequence $$n \mapsto D^rf^p_n[g]$$ n ↦ f [ g ] converges uniformly on bounded subinterval $$\mathbb {R}_+$$ ℝ + to D r