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Statements
𝐻𝑝
n
,
m
(
x
)
𝐻𝑝
n
,
m
(
y
)
=
∑
j
=
0
n
A
j
sin
2
j
θ
P
n
-
j
(
γ
+
δ
+
2
j
-
1
,
ϵ
-
1
)
(
cos
(
2
θ
)
)
P
j
(
δ
-
1
,
γ
-
1
)
(
cos
(
2
ϕ
)
)
,
Heun-polynomial-m
𝑛
𝑚
𝑎
subscript
𝑞
𝑛
𝑚
𝑛
𝛽
𝛾
𝛿
𝑥
Heun-polynomial-m
𝑛
𝑚
𝑎
subscript
𝑞
𝑛
𝑚
𝑛
𝛽
𝛾
𝛿
𝑦
superscript
subscript
𝑗
0
𝑛
subscript
𝐴
𝑗
2
𝑗
𝜃
Jacobi-polynomial-P
𝛾
𝛿
2
𝑗
1
italic-ϵ
1
𝑛
𝑗
2
𝜃
Jacobi-polynomial-P
𝛿
1
𝛾
1
𝑗
2
italic-ϕ
{\displaystyle{\displaystyle\mathit{Hp}_{n,m}\left(x\right)\mathit{Hp}_{n,m}%
\left(y\right)=\sum_{j=0}^{n}A_{j}{\sin^{2j}}\theta\*P^{(\gamma+\delta+2j-1,%
\epsilon-1)}_{n-j}\left(\cos\left(2\theta\right)\right)P^{(\delta-1,\gamma-1)}%
_{j}\left(\cos\left(2\phi\right)\right),}}
𝐻𝑝
n
,
m
(
a
,
q
n
,
m
;
-
n
,
β
,
γ
,
δ
;
z
)
Heun-polynomial-m
𝑛
𝑚
𝑎
subscript
𝑞
𝑛
𝑚
𝑛
𝛽
𝛾
𝛿
𝑧
{\displaystyle{\displaystyle\mathit{Hp}_{\NVar{n},\NVar{m}}\left(\NVar{a},%
\NVar{q_{n,m}};\NVar{-n},\NVar{\beta},\NVar{\gamma},\NVar{\delta};\NVar{z}%
\right)}}
P
n
(
α
,
β
)
(
x
)
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(%
\NVar{x}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
j
𝑗
{\displaystyle{\displaystyle j}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
a
𝑎
{\displaystyle{\displaystyle a}}
q
𝑞
{\displaystyle{\displaystyle q}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
θ
𝜃
{\displaystyle{\displaystyle\theta}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
x
𝑥
{\displaystyle{\displaystyle x}}
y
𝑦
{\displaystyle{\displaystyle y}}
A
j
subscript
𝐴
𝑗
{\displaystyle{\displaystyle A_{j}}}
Identifiers
