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Orthogonality of Legendre polynomials
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Differential equation
Ordinary differential equation
Linear ordinary differential equation
Second-order linear differential equation
Legendre differential equation
Legendre polynomial
2026-09-28
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The
Legendre polynomials
are orthogonal on
[
−
1
,
1
]
with unit
weight
:
∫
−
1
1
P
ℓ
(
x
)
P
m
(
x
)
d
x
=
2
ℓ
+
1
2
δ
ℓ
m
.
(1)
Ancestors
(10)
Legendre polynomial
Legendre differential equation
Second-order linear differential equation
Linear ordinary differential equation
Ordinary differential equation
Differential equation
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 312
/
3
/
b
/
ii
/
Solution
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