Abstract
AbstractWe consider the standard symmetric elliptic integral $$R_F(x,y,z)$$
R
F
(
x
,
y
,
z
)
for complex x, y, z. We derive convergent expansions of $$R_F(x,y,z)$$
R
F
(
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 $$\mathbb {C}{\setminus }(-\infty ,0]$$
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.
Funder
Ministerio de Economia y Competitividad
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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