A variety of problems in classical mechanics and mathematical physics lead to Picard–Fuchs equations. These equations are frequently solvable in terms of generalized hypergeometric functions, and the monodromy of generalized hypergeometric functions plays an important role in describing properties of the solutions. See, for example, Berglund et al. (1994).
A substantial transition occurs in a random graph of vertices when the number of edges becomes approximately . In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three functions are applied to compute the expected value of the excess.
Many combinatorial identities, especially ones involving binomial and related coefficients, are special cases of hypergeometric identities. In Petkovšek et al. (1996) tools are given for automated proofs of these identities.