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About the Project
19
Elliptic Integrals
Legendre’s Integrals
19.3
Graphics
19.3
Graphics
19.4
Derivatives and Differential Equations
Figure 19.3.1
(See
in context
.)
Figure 19.3.1:
K
(
k
)
and
E
(
k
)
as functions of
k
2
for
−
2
≤
k
2
≤
1
. Graphs of
K
′
(
k
)
and
E
′
(
k
)
are the mirror images in the vertical line
k
2
=
1
2
.
ⓘ
Annotations:
Symbols:
K
′
(
k
)
: Legendre’s complementary complete elliptic integral of the first kind
,
E
′
(
k
)
: Legendre’s complementary complete elliptic integral of the second kind
,
K
(
k
)
: Legendre’s complete elliptic integral of the first kind
,
E
(
k
)
: Legendre’s complete elliptic integral of the second kind
and
k
: real or complex modulus
Permalink:
http://dlmf.nist.gov/19.3.F1.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§19.3
and
Ch.19