  We first briefly discuss the relation between black hole thermodynamics and
the entropy function formalism. We find that an equation which governs the
relationship between Sen's entropy function and black hole entropy, can quickly
give higher order corrections to entropy of pure (anti-) de Sitter space
without knowing the corrected metric. We also show that near horizon geometry
and the entropy function extremization is no longer required for pure (anti-)de
Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-)
de Sitter black holes together with Gauss-Bonnet terms, $R^2$ terms and $R^4$
terms are calculated as concrete examples.
