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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 19.3.9
(See
in context
.)
3D
Help
Figure 19.3.9:
ℜ
(
K
(
k
)
)
as a function of complex
k
2
for
−
2
≤
ℜ
(
k
2
)
≤
2
,
−
2
≤
ℑ
(
k
2
)
≤
2
. The real part is symmetric under reflection in the real axis. On the branch cut (
k
2
≥
1
) it is infinite at
k
2
=
1
, and has the value
K
(
1
/
k
)
/
k
when
k
2
>
1
.
3D
Help
ⓘ
Annotations:
Symbols:
K
(
k
)
: Legendre’s complete elliptic integral of the first kind
,
ℑ
: imaginary part
,
ℜ
: real part
and
k
: real or complex modulus
Permalink:
http://dlmf.nist.gov/19.3.F9.mag
Encodings:
Magnified png
,
Vizualization
,
pdf
See also:
Annotations for
§19.3
and
Ch.19