Very incomplete documentation for the translation coefficients.

Former-commit-id: 7c707f71ac39364be7cb628c074cfb777ea61a92
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Marek Nečada 2016-07-26 06:35:27 +03:00
parent 8646b18492
commit 3171c07c3e
1 changed files with 42 additions and 0 deletions

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@ -453,6 +453,27 @@ def a_q(m,n,μ,ν,q = None):
# ZDE VYCHÁZEJÍ DIVNÁ ZNAMÉNKA
#@jit
def Ã(m,n,μ,ν,kdlj,θlj,φlj,r_ge_d,J):
"""
The à translation coefficient for spherical vector waves.
Parameters
----------
m, n: int
The indices (degree and order) of the destination basis.
μ, ν: int
The indices of the source basis wave.
kdlj, θlj, φlj: float
The spherical coordinates of the relative position of
the new center vs. the old one (R_new - R_old);
the distance has to be already multiplied by the wavenumber!
r_ge_d: TODO
J: 1, 2, 3 or 4
Type of the wave in the old center.
Returns:
--------
TODO
"""
exponent=(math.lgamma(2*n+1)-math.lgamma(n+2)+math.lgamma(2*ν+3)-math.lgamma(ν+2)
+math.lgamma(n+ν+m-μ+1)-math.lgamma(n-m+1)-math.lgamma(ν+μ+1)
+math.lgamma(n+ν+1) - math.lgamma(2*(n+ν)+1))
@ -485,6 +506,27 @@ def Ã(m,n,μ,ν,kdlj,θlj,φlj,r_ge_d,J):
# ZDE OPĚT JINAK ZNAMÉNKA než v Xu (J. comp. phys 127, 285)
#@jit
def B̃(m,n,μ,ν,kdlj,θlj,φlj,r_ge_d,J):
"""
The B̃ translation coefficient for spherical vector waves.
Parameters
----------
m, n: int
The indices (degree and order) of the destination basis.
μ, ν: int
The indices of the source basis wave.
kdlj, θlj, φlj: float
The spherical coordinates of the relative position of
the new center vs. the old one (R_new - R_old);
the distance has to be already multiplied by the wavenumber!
r_ge_d: TODO
J: 1, 2, 3 or 4
Type of the wave in the old center.
Returns:
--------
TODO
"""
exponent=(math.lgamma(2*n+3)-math.lgamma(n+2)+math.lgamma(2*ν+3)-math.lgamma(ν+2)
+math.lgamma(n+ν+m-μ+2)-math.lgamma(n-m+1)-math.lgamma(ν+μ+1)
+math.lgamma(n+ν+2) - math.lgamma(2*(n+ν)+3))