New series expansions of the 3F2 function
Fecha
2015Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión enviada / Bidali den bertsioa
Impacto
|
10.1016/j.jmaa.2014.07.065
Resumen
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 doma ...
[++]
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. [--]
Materias
Generalized hypergeometric function 3F2,
Approximation by 2F1 functions,
Convergent series expansions
Notas
Esta es la versión no revisada del artículo: José L. López, Pedro Pagola, Ester Pérez Sinusía, New series expansions of the 3F2 function. J. Math. Anal. Appl, 421 (2015) 982-995.
Pages 982-995, ISSN 0022-247X. Se puede consultar la versión publicada en https://doi.org/10.1016/j.jmaa.2014.07.065.
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Entidades Financiadoras
The authors acknowledge Dirección General de Ciencia y Tecnología (grant No. MTM2010-21037) for financial support.