46
3 Study of Electrophysical Characteristics of Blood …
where
q
0
mn =
1
n(n + 1)
∂
∂α
P
m
n (cos α) cos β − i
m
sin α
P
m
n (cos α) sin β
,
p
0
mn =
1
n(n + 1)
∂
∂α
P
m
n (cos α) cos β − i
m
sin α
P
m
n (cos α) sin β
.
In order to describe the scattering at an jth particle, we use the summation theorems
for the vector-spherical functions [7]:
M mn =
∞
ν=0
ν
μ=−ν
[AO
mn
μν M
μν + B O
mn
μν N
μν ],
N mn =
∞
ν=0
ν
μ=−ν
[B O
mn
μν M
μν + AO
mn
μν N
μν ].
M mn , N mn are the basis vector-spherical wave functions defined with the center at
the point O, M
μν , N
μν are similar functions with the center at the point O
, M
μν and
N
μν have the form identical to M mn , N mn . Here,
AO
mn
μν (l, j) = (−1)
μ i
ν−n 2ν + 1
2ν(ν + 1)
n+ν
p=|n−ν|
(−i)
p
[n(n + 1)+
+ν(ν + 1) − p( p + 1)]α(m, n, −μ, ν, p)h
1
p (kr (l, j) )×
× P
m−μ
p
(cos θ (l, j) )e
i(m−μ)φ l, j ,
(3.60)
B O
mn
μν (l, j) = (−1)
μ i
ν−n 2ν + 1
2ν(ν + 1)
n+ν
p=|n−ν|
(−i)
p b[m, n, −μ, ν, p, p − 1]×
× h
1
p (kr (l, j) )P
m−μ
p
(cos θ (l, j) )e
i(m−μ)φ l, j ,
(3.61)
b(m, n, −μ, ν, p, p − 1) =
2 p + 1
2 p − 1
[(ν − μ)(ν + μ + 1)] ×
×
2 p + 1
2 p − 1
[α(m, n, −μ − 1, ν, p − 1) − ( p − m + μ)( p − m + μ − 1)] ×
×
2 p + 1
2 p − 1
[α(m, n, −μ + 1, ν, p − 1) + 2μ( p − m + μ)] ×