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 ...

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

The rest of the article covers more specific issues related to conjugate priors for exponential families. In particular, we analyze the monotonicity of the expected posterior variance for μ with ...