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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 19.3.10
(See
in context
.)
3D
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Figure 19.3.10:
ℑ
(
K
(
k
)
)
as a function of complex
k
2
for
−
2
≤
ℜ
(
k
2
)
≤
2
,
−
2
≤
ℑ
(
k
2
)
≤
2
. The imaginary part is 0 for
k
2
<
1
, and is antisymmetric under reflection in the real axis. On the upper edge of the branch cut (
k
2
≥
1
) it has the value
K
(
k
′
)
if
k
2
>
1
, and
1
4
π
if
k
2
=
1
.
3D
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ⓘ
Annotations:
Symbols:
π
: the ratio of the circumference of a circle to its diameter
,
K
(
k
)
: Legendre’s complete elliptic integral of the first kind
,
ℑ
: imaginary part
,
ℜ
: real part
,
k
: real or complex modulus
and
k
′
: complementary modulus
Permalink:
http://dlmf.nist.gov/19.3.F10.mag
Encodings:
Magnified png
,
Vizualization
,
pdf
See also:
Annotations for
§19.3
and
Ch.19