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Geometry of Two-Variable Legendre Polynomials

​
bound for y and x
3
bound for z
10
cut position y
2
polynomial degree n
7
P
7
(x, y) =
-429
7
x
+2772
5
x
y-5040
3
x
2
y
+2240x
3
y
2048
P
7
(x) =
P
7
(x, 2) =
-429
7
x
+5544
5
x
-20160
3
x
+17920x
2048
On the left is a three-dimensional plot of a Legendre polynomial in two variables
x
and
y
; on the right is a two-dimensional plot of the surface cut by a plane perpendicular to the
y
axis. The exponential operator transform is defined in the Details.
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