Generalization of Schlafli formula to the volume of a spherically faced simplex
arXiv:1710.10735
Abstract
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.
37 pages, 2 figures