Elliptic integrals and functions.
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__init__(self,
k2=0,
alpha2=0,
kp2=None,
alphap2=None,
name='')
Constructor, specifying the modulus and
parameter. |
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deltaD(self,
sn,
cn,
dn)
Jahnke's periodic incomplete elliptic integral. |
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deltaE(self,
sn,
cn,
dn)
The periodic incomplete integral of the second kind. |
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deltaEinv(self,
stau,
ctau)
The periodic inverse of the incomplete integral of the second kind. |
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deltaF(self,
sn,
cn,
dn)
The periodic incomplete integral of the first kind. |
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deltaG(self,
sn,
cn,
dn)
Legendre's periodic geodesic longitude integral. |
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deltaH(self,
sn,
cn,
dn)
Cayley's periodic geodesic longitude difference integral. |
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deltaPi(self,
sn,
cn,
dn)
The periodic incomplete integral of the third kind. |
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fD(self,
phi_or_sn,
cn=None,
dn=None)
Jahnke's incomplete elliptic integral in terms of Jacobi elliptic
functions. |
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fDelta(self,
sn,
cn)
The Delta amplitude function. |
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fE(self,
phi_or_sn,
cn=None,
dn=None)
The incomplete integral of the second kind in terms of Jacobi
elliptic functions. |
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fEd(self,
deg)
The incomplete integral of the second kind with the argument given in
degrees. |
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fEinv(self,
x)
The inverse of the incomplete integral of the second kind. |
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fF(self,
phi_or_sn,
cn=None,
dn=None)
The incomplete integral of the first kind in terms of Jacobi elliptic
functions. |
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fG(self,
phi_or_sn,
cn=None,
dn=None)
Legendre's geodesic longitude integral in terms of Jacobi elliptic
functions. |
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fH(self,
phi_or_sn,
cn=None,
dn=None)
Cayley's geodesic longitude difference integral in terms of Jacobi
elliptic functions. |
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fPi(self,
phi_or_sn,
cn=None,
dn=None)
The incomplete integral of the third kind in terms of Jacobi elliptic
functions. |
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reset(self,
k2=0,
alpha2=0,
kp2=None,
alphap2=None)
Reset the modulus, parameter and the complementaries. |
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sncndn(self,
x)
The Jacobi elliptic function. |
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Inherited from named._Named:
__imatmul__,
__matmul__,
__repr__,
__rmatmul__,
__str__,
attrs,
classof,
copy,
dup,
methodname,
rename,
toRepr,
toStr,
toStr2
Inherited from object:
__delattr__,
__format__,
__getattribute__,
__hash__,
__new__,
__reduce__,
__reduce_ex__,
__setattr__,
__sizeof__,
__subclasshook__
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fRC(x,
y)
Degenerate symmetric integral of the first kind RC(x,
y). |
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fRD(x,
y,
z,
*over)
Degenerate symmetric integral of the third kind RD(x, y,
z). |
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fRF(x,
y,
z=0)
Symmetric or complete symmetric integral of the first kind
RF(x, y, z) respectively RF(x, y). |
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fRG(x,
y,
z=0)
Symmetric or complete symmetric integral of the second kind
RG(x, y, z) respectively RG(x, y). |
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fRJ(x,
y,
z,
p)
Symmetric integral of the third kind RJ(x, y, z, p). |
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alpha2
Get α^2, the square of the parameter (float).
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alphap2
Get α'^2, the square of the complementary parameter
(float).
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cD
Get Jahnke's complete integral D(k)
(float), defined.
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cE
Get the complete integral of the second kind E(k)
(float), defined.
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cG
Get Legendre's complete geodesic longitude integral G(α^2,
k) (float).
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cH
Get Cayley's complete geodesic longitude difference integral
H(α^2, k) (float).
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cK
Get the complete integral of the first kind K(k)
(float), defined.
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cKE
Get the difference between the complete integrals of the first and
second kinds, K(k) − E(k) (float).
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cPi
Get the complete integral of the third kind Pi(α^2, k)
(float), defined.
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eps
Get epsilon (float).
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k2
Get k^2, the square of the modulus (float).
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kp2
Get k'^2, the square of the complementary modulus
(float).
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Inherited from named._Named:
classname,
classnaming,
iteration,
name,
named,
named2,
named3,
named4,
sizeof
Inherited from object:
__class__
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