How to check whether Laguerre polynomials are orthogonal?











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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.










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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















up vote
4
down vote

favorite
1












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.










share|improve this question









New contributor




Crunchy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • 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













up vote
4
down vote

favorite
1









up vote
4
down vote

favorite
1






1





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.










share|improve this question









New contributor




Crunchy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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






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share|improve this question









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share|improve this question




share|improve this question








edited Nov 29 at 16:23









m_goldberg

83.9k870193




83.9k870193






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asked Nov 29 at 4:17









Crunchy

211




211




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New contributor





Crunchy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






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Check out our Code of Conduct.












  • 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










  • 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










2 Answers
2






active

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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}]


enter image description here






share|improve this answer






























    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.}}




    $left(
    begin{array}{cccccccccc}
    1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
    0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
    0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
    0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
    0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
    0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
    0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
    0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
    0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
    0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
    end{array}
    right)$






    share|improve this answer





















    • 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











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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

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    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}]


    enter image description here






    share|improve this answer



























      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}]


      enter image description here






      share|improve this answer

























        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}]


        enter image description here






        share|improve this answer














        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}]


        enter image description here







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited Nov 29 at 5:26

























        answered Nov 29 at 5:01









        kglr

        174k9196402




        174k9196402






















            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.}}




            $left(
            begin{array}{cccccccccc}
            1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
            end{array}
            right)$






            share|improve this answer





















            • 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















            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.}}




            $left(
            begin{array}{cccccccccc}
            1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
            end{array}
            right)$






            share|improve this answer





















            • 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













            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.}}




            $left(
            begin{array}{cccccccccc}
            1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
            end{array}
            right)$






            share|improve this answer












            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.}}




            $left(
            begin{array}{cccccccccc}
            1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. & 0 \
            0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1. \
            end{array}
            right)$







            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered Nov 29 at 4:57









            That Gravity Guy

            2,0911515




            2,0911515












            • 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


















            • 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
















            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










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