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19
Elliptic Integrals
Symmetric Integrals
19.17
Graphics
19.17
Graphics
19.18
Derivatives and Differential Equations
Figure 19.17.7
(See
in context
.)
Figure 19.17.7:
Cauchy principal value of
R
J
(
0.5
,
y
,
1
,
p
)
for
y
=
0
,
0.01
,
0.05
,
0.2
,
1
,
−
1
≤
p
<
0
.
y
=
1
corresponds to
3
(
R
C
(
0.5
,
p
)
−
(
π
/
8
)
)
/
(
1
−
p
)
. As
p
→
0
the curve for
y
=
0
has the finite limit
−
8.10386
…
; see (
19.20.10
).
ⓘ
Annotations:
Symbols:
R
C
(
x
,
y
)
: Carlson’s combination of inverse circular and inverse hyperbolic functions
,
R
J
(
x
,
y
,
z
,
p
)
: symmetric elliptic integral of third kind
and
π
: the ratio of the circumference of a circle to its diameter
Permalink:
http://dlmf.nist.gov/19.17.F7.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§19.17
and
Ch.19
