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subject to
K
=
π/
2
0
, K
=
π/
2
0
d
φ
d
φ
1
1
k
2
)sin
2
φ
.
(C.36)
k
2
sin
2
φ
−
(1
−
−
End of Lemma.
These notes on elliptic functions and elliptic integrals are by no means sucient to get some
in-sight into these special functions. For numerical calculations based upon the
Landen trans-
formation
, we refer to
Bulirsch
(
1965a
,
b
,
1969a
,
b
),
Gerstl
(
1984
), and
Kneser
(
1928
). General
references are
Abramowitz and Stegun
(
1972
),
Ayoub
(
1984
),
Bellman
(
1961
),
Cooke
(
1994
),
Dumont
(
1981
),
Fricke
(
1913
),
Porter
(
1989
),
Press et al.
(
1992
),
Rosen
(
1981
),
Schett
(
1977
),
Slavutin
(
1973
),
Sorokina
(
1983
),
Spanier and Oldham
(
1987
),
Stillwell
(
1989
),
Toelke
(
1967
),
and
Tricomi
(
1948
).
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