Insights into electrochemical behavior and kinetics of NiP on PEDOT:PSS/reduced graphene oxide as high-performance electrodes for alkaline urea oxidation

Journal of Solid State Electrochemistry - Highly efficient, abundant, and low-cost materials are highly demanded for energy conversion applications to address the rising consumption of energy. In...     

Special function representations of the Poisson kernel on hyperbolic spaces

In this paper we compute explicit formulae for the Poisson kernels on the hyperbolic upper half-space \(\mathbf {H}^{n}\) and the Poincaré unit ball \(\mathbf {D}^{n}\). We first construct an associated Legendre function expression for eigenfunctions of the Laplacian and use superposition principle to get a solution for the Laplace equation on \(\mathbf {H}^{n}\). The Poisson kernel on \(\mathbf {D}^{n}\) is obtained from that on \(\mathbf {H}^{n}\) by letting the hyperbolic distance \(\rho =d(w,w')\) \((w,w'\in \mathbf {H}^{n})\) tend to infinity. These Poisson kernels, apart from being interesting in their own right lead to various identities that seem to be novel in the context of special functions.