The purpose of this paper is to present a variational formula of Schläfli type for the volume of a spherically faced simplex in the Euclidean space. It is described in terms of Cayley–Menger determinants and their differentials involved with hypersphere arrangements. We derive it as a limit of fundamental identities for hypergeometric integrals associated with hypersphere arrangements obtained by the authors in the preceding article.
Kazuhiko AOMOTO. Yoshinori MACHIDA. "Generalization of Schläfli formula to the volume of a spherically faced simplex." J. Math. Soc. Japan 72 (1) 213 - 249, January, 2020. https://doi.org/10.2969/jmsj/80238023