ÇETİNKAYA, ASENAKarp, DmitriiPrilepkina, Elena2023-01-062023-01-062021Çetinkaya, A., Karp, D., & Prilepkina, E. (2021). Hypergeometric functions at unit argument: simple derivation of old and new identities.1815-0659https://doi.org/10.3842/SIGMA.2021.098https://hdl.handle.net/11413/8178The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hyper-geometric functions from the symmetries and other properties of Meijer's G function. For instance, we recover two- and three-term Thomae relations for F-3(2), give two- and three-term transformations for F-4(3) with one unit shift and F-5(4) with two unit shifts in the parameters, establish multi-term identities for general F-p(p-1) and several transformations for terminating Kampe de Feriet and Srivastava F-(3) functions. We further present a presumably new formula for analytic continuation of F-p(p-1)(1) in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and q-hypergeometric functions to derive multi-term relations for terminating series.eninfo:eu-repo/semantics/openAccessGeneralized Hypergeometric FunctionMeijer's G FunctionMultiple Hypergeometric SeriesKampé De Fériet FunctionSrivastava FunctionHypergeometric IdentityGeneralized Bernoulli PolynomialsArticle000717803500001