Publication: New series expansions of the 3F2 function
Consultable a partir de
Date
2015
Director
Publisher
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión enviada / Bidali den bertsioa
Project identifier
Abstract
We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. Some of these expansions involve the polynomial 3F2(a1,−n, a3; b1, b2; z) evaluated at certain points z. Other expansions involve the Gauss hypergeometric function 2F1. The domain of convergence is sometimes a disk, other times a half-plane, other times the region |z|2 < 4|1 − z|. The accuracy of the approximation given by these expansions is illustrated with numerical experiments.
Keywords
Generalized hypergeometric function 3F2, Approximation by 2F1 functions, Convergent series expansions
Department
Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza
Faculty/School
Degree
Doctorate program
Editor version
Funding entities
The authors acknowledge Dirección General de Ciencia y Tecnología (grant No. MTM2010-21037) for financial support.
Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.