Bujanda Cirauqui, BlancaLópez García, José LuisPagola Martínez, Pedro JesúsPalacios Herrero, Pablo2022-01-172022-01-1720221578-730310.1007/s13398-021-01151-yhttps://academica-e.unavarra.es/handle/2454/41789We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of C\ (−∞, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples.17 p.application/pdfeng© The Author(s) 2021. Creative Commons Attribution 4.0 International LicenseConvergent expansionsError boundsSymmetric standard elliptic integralsUniform expansionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia