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3.3.E1
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MaRDI QID
Q1076
Label: 3.3.E1
Digital Library of Mathematical Functions ID
3.3.E1
P
n
(
z
)
=
∑
k
=
0
n
ℓ
k
(
z
)
f
k
=
∑
k
=
0
n
ω
n
+
1
(
z
)
(
z
-
z
k
)
ω
n
+
1
′
(
z
k
)
f
k
,
subscript
𝑃
𝑛
𝑧
superscript
subscript
𝑘
0
𝑛
subscript
ℓ
𝑘
𝑧
subscript
𝑓
𝑘
superscript
subscript
𝑘
0
𝑛
subscript
𝜔
𝑛
1
𝑧
𝑧
subscript
𝑧
𝑘
superscript
subscript
𝜔
𝑛
1
′
subscript
𝑧
𝑘
subscript
𝑓
𝑘
{\displaystyle{\displaystyle P_{n}(z)=\sum_{k=0}^{n}\ell_{k}(z)f_{k}=\sum_{k=0% }^{n}\frac{\omega_{n+1}(z)}{(z-z_{k})\omega_{n+1}^{\prime}(z_{k})}f_{k},}}
Constraint(s)
Symbols List
ℓ
k
(
z
)
subscript
ℓ
𝑘
𝑧
{\displaystyle{\displaystyle\ell_{k}(z)}}
: Lagrange interpolation polynomial
ω
n
+
1
(
z
)
subscript
𝜔
𝑛
1
𝑧
{\displaystyle{\displaystyle\omega_{n+1}(z)}}
: nodal polynomial (locally)
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