How to check whether Laguerre polynomials are orthogonal?
up vote
4
down vote
favorite
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. Something like:
M=Integrate[LaguerreL[i,x] LaguerreL[j,x] Exp[-x], {x,0,Infinity}]
And in the end I have to draw the dynamic drawing of these polynomials so that if I choose on graph n, from 0 to 20, the correct polynomial will be drawn with its derivative.
calculus-and-analysis polynomials homework
add a comment |
up vote
4
down vote
favorite
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. Something like:
M=Integrate[LaguerreL[i,x] LaguerreL[j,x] Exp[-x], {x,0,Infinity}]
And in the end I have to draw the dynamic drawing of these polynomials so that if I choose on graph n, from 0 to 20, the correct polynomial will be drawn with its derivative.
calculus-and-analysis polynomials homework
Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Table[M, {i, 10}, {j, 10}]
?
– Michael E2
Nov 29 at 4:45
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
1
That's not the problem....
– Michael E2
Nov 29 at 5:20
add a comment |
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. Something like:
M=Integrate[LaguerreL[i,x] LaguerreL[j,x] Exp[-x], {x,0,Infinity}]
And in the end I have to draw the dynamic drawing of these polynomials so that if I choose on graph n, from 0 to 20, the correct polynomial will be drawn with its derivative.
calculus-and-analysis polynomials homework
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. Something like:
M=Integrate[LaguerreL[i,x] LaguerreL[j,x] Exp[-x], {x,0,Infinity}]
And in the end I have to draw the dynamic drawing of these polynomials so that if I choose on graph n, from 0 to 20, the correct polynomial will be drawn with its derivative.
calculus-and-analysis polynomials homework
calculus-and-analysis polynomials homework
edited Nov 29 at 16:23
m_goldberg
84k870193
84k870193
asked Nov 29 at 4:17
Crunchy
211
211
Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Table[M, {i, 10}, {j, 10}]
?
– Michael E2
Nov 29 at 4:45
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
1
That's not the problem....
– Michael E2
Nov 29 at 5:20
add a comment |
Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Table[M, {i, 10}, {j, 10}]
?
– Michael E2
Nov 29 at 4:45
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
1
That's not the problem....
– Michael E2
Nov 29 at 5:20
Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Table[M, {i, 10}, {j, 10}]
?– Michael E2
Nov 29 at 4:45
Table[M, {i, 10}, {j, 10}]
?– Michael E2
Nov 29 at 4:45
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
1
1
That's not the problem....
– Michael E2
Nov 29 at 5:20
That's not the problem....
– Michael E2
Nov 29 at 5:20
add a comment |
2 Answers
2
active
oldest
votes
up vote
6
down vote
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
n = 10;
Outer[Integrate[LaguerreL[#, x] LaguerreL[#2, x] Exp[-x], {x, 0, ∞}] &,
Range[n], Range[n]] == IdentityMatrix[n]
True
Manipulate[Show[Plot[Evaluate@LaguerreL[Sort@n, x], {x, 0, 10},
PlotLegends -> ("LaguerreL[" <> ToString[#] <> ", x]" & /@ Sort[n]),
PlotRange -> {-15, 15}],
Plot[Evaluate[D[LaguerreL[Sort@n, z], z] /. z -> x], {x, 0, 10},
PlotLegends -> ("D[LaguerreL[" <> ToString[#] <> ", x], x]" & /@ Sort[n]),
PlotStyle -> Dashed]],
{{n, {5, 10, 17}}, Range[0,20], TogglerBar}]
add a comment |
up vote
3
down vote
Table[
NIntegrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity}],
{i, 10},
{j, 10}
] // Chop // Quiet
MatrixForm@%
Manipulate[
Plot[
{#, D[#, x]} &@LaguerreL[n, x] // Evaluate,
{x, 0, 10},
Frame -> True,
BaseStyle -> {11, FontFamily -> Times},
PlotLabel -> StringForm["n=``", n]
],
{n, 0, 20, 1, PopupMenu}
]
{{1., 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0, 0, 0}, {0,
0, 1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1., 0, 0, 0, 0, 0, 0}, {0,
0, 0, 0, 1., 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1., 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0, 1., 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1., 0, 0}, {0, 0,
0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1.}}
$left(
begin{array}{cccccccccc}
1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
end{array}
right)$
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just changePlot[{#, D[#, x]} &@LaguerreL[n, x]
toPlot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.
– That Gravity Guy
Nov 29 at 20:47
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
n = 10;
Outer[Integrate[LaguerreL[#, x] LaguerreL[#2, x] Exp[-x], {x, 0, ∞}] &,
Range[n], Range[n]] == IdentityMatrix[n]
True
Manipulate[Show[Plot[Evaluate@LaguerreL[Sort@n, x], {x, 0, 10},
PlotLegends -> ("LaguerreL[" <> ToString[#] <> ", x]" & /@ Sort[n]),
PlotRange -> {-15, 15}],
Plot[Evaluate[D[LaguerreL[Sort@n, z], z] /. z -> x], {x, 0, 10},
PlotLegends -> ("D[LaguerreL[" <> ToString[#] <> ", x], x]" & /@ Sort[n]),
PlotStyle -> Dashed]],
{{n, {5, 10, 17}}, Range[0,20], TogglerBar}]
add a comment |
up vote
6
down vote
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
n = 10;
Outer[Integrate[LaguerreL[#, x] LaguerreL[#2, x] Exp[-x], {x, 0, ∞}] &,
Range[n], Range[n]] == IdentityMatrix[n]
True
Manipulate[Show[Plot[Evaluate@LaguerreL[Sort@n, x], {x, 0, 10},
PlotLegends -> ("LaguerreL[" <> ToString[#] <> ", x]" & /@ Sort[n]),
PlotRange -> {-15, 15}],
Plot[Evaluate[D[LaguerreL[Sort@n, z], z] /. z -> x], {x, 0, 10},
PlotLegends -> ("D[LaguerreL[" <> ToString[#] <> ", x], x]" & /@ Sort[n]),
PlotStyle -> Dashed]],
{{n, {5, 10, 17}}, Range[0,20], TogglerBar}]
add a comment |
up vote
6
down vote
up vote
6
down vote
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
n = 10;
Outer[Integrate[LaguerreL[#, x] LaguerreL[#2, x] Exp[-x], {x, 0, ∞}] &,
Range[n], Range[n]] == IdentityMatrix[n]
True
Manipulate[Show[Plot[Evaluate@LaguerreL[Sort@n, x], {x, 0, 10},
PlotLegends -> ("LaguerreL[" <> ToString[#] <> ", x]" & /@ Sort[n]),
PlotRange -> {-15, 15}],
Plot[Evaluate[D[LaguerreL[Sort@n, z], z] /. z -> x], {x, 0, 10},
PlotLegends -> ("D[LaguerreL[" <> ToString[#] <> ", x], x]" & /@ Sort[n]),
PlotStyle -> Dashed]],
{{n, {5, 10, 17}}, Range[0,20], TogglerBar}]
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
n = 10;
Outer[Integrate[LaguerreL[#, x] LaguerreL[#2, x] Exp[-x], {x, 0, ∞}] &,
Range[n], Range[n]] == IdentityMatrix[n]
True
Manipulate[Show[Plot[Evaluate@LaguerreL[Sort@n, x], {x, 0, 10},
PlotLegends -> ("LaguerreL[" <> ToString[#] <> ", x]" & /@ Sort[n]),
PlotRange -> {-15, 15}],
Plot[Evaluate[D[LaguerreL[Sort@n, z], z] /. z -> x], {x, 0, 10},
PlotLegends -> ("D[LaguerreL[" <> ToString[#] <> ", x], x]" & /@ Sort[n]),
PlotStyle -> Dashed]],
{{n, {5, 10, 17}}, Range[0,20], TogglerBar}]
edited Nov 29 at 5:26
answered Nov 29 at 5:01
kglr
175k9197402
175k9197402
add a comment |
add a comment |
up vote
3
down vote
Table[
NIntegrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity}],
{i, 10},
{j, 10}
] // Chop // Quiet
MatrixForm@%
Manipulate[
Plot[
{#, D[#, x]} &@LaguerreL[n, x] // Evaluate,
{x, 0, 10},
Frame -> True,
BaseStyle -> {11, FontFamily -> Times},
PlotLabel -> StringForm["n=``", n]
],
{n, 0, 20, 1, PopupMenu}
]
{{1., 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0, 0, 0}, {0,
0, 1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1., 0, 0, 0, 0, 0, 0}, {0,
0, 0, 0, 1., 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1., 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0, 1., 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1., 0, 0}, {0, 0,
0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1.}}
$left(
begin{array}{cccccccccc}
1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
end{array}
right)$
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just changePlot[{#, D[#, x]} &@LaguerreL[n, x]
toPlot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.
– That Gravity Guy
Nov 29 at 20:47
add a comment |
up vote
3
down vote
Table[
NIntegrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity}],
{i, 10},
{j, 10}
] // Chop // Quiet
MatrixForm@%
Manipulate[
Plot[
{#, D[#, x]} &@LaguerreL[n, x] // Evaluate,
{x, 0, 10},
Frame -> True,
BaseStyle -> {11, FontFamily -> Times},
PlotLabel -> StringForm["n=``", n]
],
{n, 0, 20, 1, PopupMenu}
]
{{1., 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0, 0, 0}, {0,
0, 1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1., 0, 0, 0, 0, 0, 0}, {0,
0, 0, 0, 1., 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1., 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0, 1., 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1., 0, 0}, {0, 0,
0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1.}}
$left(
begin{array}{cccccccccc}
1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
end{array}
right)$
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just changePlot[{#, D[#, x]} &@LaguerreL[n, x]
toPlot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.
– That Gravity Guy
Nov 29 at 20:47
add a comment |
up vote
3
down vote
up vote
3
down vote
Table[
NIntegrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity}],
{i, 10},
{j, 10}
] // Chop // Quiet
MatrixForm@%
Manipulate[
Plot[
{#, D[#, x]} &@LaguerreL[n, x] // Evaluate,
{x, 0, 10},
Frame -> True,
BaseStyle -> {11, FontFamily -> Times},
PlotLabel -> StringForm["n=``", n]
],
{n, 0, 20, 1, PopupMenu}
]
{{1., 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0, 0, 0}, {0,
0, 1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1., 0, 0, 0, 0, 0, 0}, {0,
0, 0, 0, 1., 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1., 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0, 1., 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1., 0, 0}, {0, 0,
0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1.}}
$left(
begin{array}{cccccccccc}
1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
end{array}
right)$
Table[
NIntegrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity}],
{i, 10},
{j, 10}
] // Chop // Quiet
MatrixForm@%
Manipulate[
Plot[
{#, D[#, x]} &@LaguerreL[n, x] // Evaluate,
{x, 0, 10},
Frame -> True,
BaseStyle -> {11, FontFamily -> Times},
PlotLabel -> StringForm["n=``", n]
],
{n, 0, 20, 1, PopupMenu}
]
{{1., 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0, 0, 0}, {0,
0, 1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1., 0, 0, 0, 0, 0, 0}, {0,
0, 0, 0, 1., 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1., 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0, 1., 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1., 0, 0}, {0, 0,
0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1.}}
$left(
begin{array}{cccccccccc}
1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
end{array}
right)$
answered Nov 29 at 4:57
That Gravity Guy
2,1011515
2,1011515
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just changePlot[{#, D[#, x]} &@LaguerreL[n, x]
toPlot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.
– That Gravity Guy
Nov 29 at 20:47
add a comment |
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just changePlot[{#, D[#, x]} &@LaguerreL[n, x]
toPlot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.
– That Gravity Guy
Nov 29 at 20:47
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
Thank you! :) Can this graph be simply modified? For example, when I increase n, on the graph will be shown graphs 1,2,3 to n, all of them on one graph?
– Crunchy
Nov 29 at 6:14
@Crunchy Sure, just change
Plot[{#, D[#, x]} &@LaguerreL[n, x]
to Plot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.– That Gravity Guy
Nov 29 at 20:47
@Crunchy Sure, just change
Plot[{#, D[#, x]} &@LaguerreL[n, x]
to Plot[{#, D[#, x]} &@LaguerreL[Range[0, n], x]
. Though, it starts to look a little chaotic even at n=4. At that point, I would go with @kglr's implementation.– That Gravity Guy
Nov 29 at 20:47
add a comment |
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Related: mathematica.stackexchange.com/questions/155030/…
– Michael E2
Nov 29 at 4:44
Table[M, {i, 10}, {j, 10}]
?– Michael E2
Nov 29 at 4:45
I have to integrate by exp(-x)dx instead of dx.
– Crunchy
Nov 29 at 4:57
1
That's not the problem....
– Michael E2
Nov 29 at 5:20