Generalization of Schlafli formula to the volume of a spherically faced simplex

30 Oct 2017 · Aomoto Kazuhiko, Machida Yoshinori ·

We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials involved with hypersphere arrangements. They are derived as a limit of fundamental identities for hypergeometric integrals.