polynomialFactory( Laplace = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Laplace name=Laplace dimension=1 lambda=1 mu=0 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,0,0],class=Point name=Unnamed dimension=3 values=[1,0,-2]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,2] isElliptical=true )
Laplace  polynomial( 0 )= 1
Laplace  polynomial( 1 )= 0.707107 * X
Laplace  polynomial( 2 )= -0.447214 + 0.223607 * X^2
Laplace  polynomial( 3 )= -0.57735 * X + 0.0481125 * X^3
Laplace  polynomial( 4 )= 0.329735 - 0.25646 * X^2 + 0.00763275 * X^4
Laplace  polynomial( 4 ) roots= [-5.67987,-1.15719,1.15719,5.67987]
Laplace  polynomial( 4 ) nodes= [-5.67987,-1.15719,1.15719,5.67987]  and weights= [0.0106869,0.489313,0.489313,0.0106869]
M=
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[[ 1 0 0 0 0 ]
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 [ 0 0 0 0 1 ]]
polynomialFactory( Logistic = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Logistic name=Logistic dimension=1 alpha=0 beta=1 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,0,0],class=Point name=Unnamed dimension=3 values=[1,0,-3.28987]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,3.28987] isElliptical=true )
Logistic  polynomial( 0 )= 1
Logistic  polynomial( 1 )= 0.551329 * X
Logistic  polynomial( 2 )= -0.559017 + 0.169921 * X^2
Logistic  polynomial( 3 )= -0.491265 * X + 0.035554 * X^3
Logistic  polynomial( 4 )= 0.421875 - 0.205809 * X^2 + 0.00561421 * X^4
Logistic  polynomial( 4 ) roots= [-5.87189,-1.47628,1.47628,5.87189]
Logistic  polynomial( 4 ) nodes= [-5.87189,-1.47628,1.47628,5.87189]  and weights= [0.0171899,0.48281,0.48281,0.0171899]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Normal = class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=HermiteFactory measure=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] )
Normal  polynomial( 0 )= 1
Normal  polynomial( 1 )= X
Normal  polynomial( 2 )= -0.707107 + 0.707107 * X^2
Normal  polynomial( 3 )= -1.22474 * X + 0.408248 * X^3
Normal  polynomial( 4 )= 0.612372 - 1.22474 * X^2 + 0.204124 * X^4
Normal  polynomial( 4 ) roots= [-2.33441,-0.741964,0.741964,2.33441]
Normal  polynomial( 4 ) nodes= [-2.33441,-0.741964,0.741964,2.33441]  and weights= [0.0458759,0.454124,0.454124,0.0458759]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Normal = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-1,0],class=Point name=Unnamed dimension=3 values=[1,-1,-1]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,1] isElliptical=true )
Normal  polynomial( 0 )= 1
Normal  polynomial( 1 )= -1 + X
Normal  polynomial( 2 )= -1.41421 * X + 0.707107 * X^2
Normal  polynomial( 3 )= 0.816497 + 2.89382e-11 * X - 1.22474 * X^2 + 0.408248 * X^3
Normal  polynomial( 4 )= -0.408248 + 1.63299 * X + 4.02503e-10 * X^2 - 0.816497 * X^3 + 0.204124 * X^4
Normal  polynomial( 4 ) roots= [-1.33441,0.258036,1.74196,3.33441]
Normal  polynomial( 4 ) nodes= [-1.33441,0.258036,1.74196,3.33441]  and weights= [0.0458759,0.454124,0.454124,0.0458759]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Rayleigh = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Rayleigh name=Rayleigh dimension=1 sigma=1 gamma=0 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-1.25331,0],class=Point name=Unnamed dimension=3 values=[1,-1.66678,-0.429204]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,0.429204] isElliptical=false )
Rayleigh  polynomial( 0 )= 1
Rayleigh  polynomial( 1 )= -1.91306 + 1.5264 * X
Rayleigh  polynomial( 2 )= 2.84565 - 5.00639 * X + 1.71446 * X^2
Rayleigh  polynomial( 3 )= -3.78384 + 10.859 * X - 7.93394 * X^2 + 1.60694 * X^3
Rayleigh  polynomial( 4 )= 4.72402 - 19.4426 * X + 22.5685 * X^2 - 9.59251 * X^3 + 1.32173 * X^4
Rayleigh  polynomial( 4 ) roots= [0.396121,1.17673,2.20107,3.48361]
Rayleigh  polynomial( 4 ) nodes= [0.396121,1.17673,2.20107,3.48361]  and weights= [0.227998,0.538465,0.221578,0.0119592]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Student = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Student name=Student dimension=1 nu=22 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,0,0],class=Point name=Unnamed dimension=3 values=[1,0,-1.1]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,1.1] isElliptical=true )
Student  polynomial( 0 )= 1
Student  polynomial( 1 )= 0.953463 * X
Student  polynomial( 2 )= -0.654654 + 0.59514 * X^2
Student  polynomial( 3 )= -1.01929 * X + 0.277989 * X^3
Student  polynomial( 4 )= 0.51299 - 0.839438 * X^2 + 0.10175 * X^4
Student  polynomial( 4 ) roots= [-2.75415,-0.815266,0.815266,2.75415]
Student  polynomial( 4 ) nodes= [-2.75415,-0.815266,0.815266,2.75415]  and weights= [0.0314522,0.468548,0.468548,0.0314522]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Triangular = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Triangular name=Triangular dimension=1 a=-1 m=0.3 b=1 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-0.1,0],class=Point name=Unnamed dimension=3 values=[1,0.0153398,-0.171667]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,0.171667] isElliptical=false )
Triangular  polynomial( 0 )= 1
Triangular  polynomial( 1 )= -0.241355 + 2.41355 * X
Triangular  polynomial( 2 )= -0.877334 - 0.428839 * X + 5.06542 * X^2
Triangular  polynomial( 3 )= 0.259575 - 4.13679 * X - 1.01753 * X^2 + 10.3656 * X^3
Triangular  polynomial( 4 )= 0.878133 + 0.925615 * X - 13.5192 * X^2 - 1.99648 * X^3 + 21.1809 * X^4
Triangular  polynomial( 4 ) roots= [-0.742936,-0.235772,0.310364,0.762603]
Triangular  polynomial( 4 ) nodes= [-0.742936,-0.235772,0.310364,0.762603]  and weights= [0.0810886,0.334646,0.456437,0.127828]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Uniform = class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1 )
Uniform  polynomial( 0 )= 1
Uniform  polynomial( 1 )= 1.73205 * X
Uniform  polynomial( 2 )= -1.11803 + 3.3541 * X^2
Uniform  polynomial( 3 )= -3.96863 * X + 6.61438 * X^3
Uniform  polynomial( 4 )= 1.125 - 11.25 * X^2 + 13.125 * X^4
Uniform  polynomial( 4 ) roots= [-0.861136,-0.339981,0.339981,0.861136]
Uniform  polynomial( 4 ) nodes= [-0.861136,-0.339981,0.339981,0.861136]  and weights= [0.173927,0.326073,0.326073,0.173927]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Uniform = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Uniform name=Uniform dimension=1 a=-1 b=3 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-1,0],class=Point name=Unnamed dimension=3 values=[1,-1,-1.33333]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,1.33333] isElliptical=true )
Uniform  polynomial( 0 )= 1
Uniform  polynomial( 1 )= -0.866025 + 0.866025 * X
Uniform  polynomial( 2 )= -0.279508 - 1.67705 * X + 0.838525 * X^2
Uniform  polynomial( 3 )= 1.15752 + 0.496078 * X - 2.48039 * X^2 + 0.826797 * X^3
Uniform  polynomial( 4 )= -0.867188 + 2.34375 * X + 2.10938 * X^2 - 3.28125 * X^3 + 0.820313 * X^4
Uniform  polynomial( 4 ) roots= [-0.722273,0.320038,1.67996,2.72227]
Uniform  polynomial( 4 ) nodes= [-0.722273,0.320038,1.67996,2.72227]  and weights= [0.173927,0.326073,0.326073,0.173927]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Weibull = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Weibull name=Weibull dimension=1 alpha=1 beta=3 gamma=0 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-0.89298,0],class=Point name=Unnamed dimension=3 values=[1,-0.947537,-0.105333]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,0.105333] isElliptical=false )
Weibull  polynomial( 0 )= 1
Weibull  polynomial( 1 )= -2.75144 + 3.08119 * X
Weibull  polynomial( 2 )= 5.3921 - 13.3967 * X + 7.27876 * X^2
Weibull  polynomial( 3 )= -8.91794 + 36.5275 * X - 42.8504 * X^2 + 14.9827 * X^3
Weibull  polynomial( 4 )= 13.3264 - 79.2309 * X + 149.529 * X^2 - 111.023 * X^3 + 28.1044 * X^4
Weibull  polynomial( 4 ) roots= [0.315842,0.737023,1.19993,1.69759]
Weibull  polynomial( 4 ) nodes= [0.315842,0.737023,1.19993,1.69759]  and weights= [0.109605,0.491205,0.364361,0.03483]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Beta = class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=JacobiFactory alpha=1 beta=0 measure=class=Beta name=Beta dimension=1 r=1 t=3 a=-1 b=1 )
Beta  polynomial( 0 )= 1
Beta  polynomial( 1 )= 0.707107 + 2.12132 * X
Beta  polynomial( 2 )= -0.866025 + 1.73205 * X + 4.33013 * X^2
Beta  polynomial( 3 )= -0.75 - 3.75 * X + 3.75 * X^2 + 8.75 * X^3
Beta  polynomial( 4 )= 0.838525 - 3.3541 * X - 11.7394 * X^2 + 7.82624 * X^3 + 17.609 * X^4
Beta  polynomial( 4 ) roots= [-0.885792,-0.446314,0.167181,0.72048]
Beta  polynomial( 4 ) nodes= [-0.885792,-0.446314,0.167181,0.72048]  and weights= [0.271014,0.406929,0.259695,0.0623619]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Beta = class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=ChebychevFactory measure=class=Arcsine name=Arcsine dimension=1 a=-1 b=1 )
Beta  polynomial( 0 )= 1
Beta  polynomial( 1 )= 1.41421 * X
Beta  polynomial( 2 )= -1.41421 + 2.82843 * X^2
Beta  polynomial( 3 )= -4.24264 * X + 5.65685 * X^3
Beta  polynomial( 4 )= 1.41421 - 11.3137 * X^2 + 11.3137 * X^4
Beta  polynomial( 4 ) roots= [-0.92388,-0.382683,0.382683,0.92388]
Beta  polynomial( 4 ) nodes= [-0.92388,-0.382683,0.382683,0.92388]  and weights= [0.25,0.25,0.25,0.25]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Beta = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Beta name=Beta dimension=1 r=0.5 t=1 a=-2 b=3 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-0.5,0],class=Point name=Unnamed dimension=3 values=[1,-0.5,-3.125]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,3.125] isElliptical=true )
Beta  polynomial( 0 )= 1
Beta  polynomial( 1 )= -0.282843 + 0.565685 * X
Beta  polynomial( 2 )= -1.30108 - 0.452548 * X + 0.452548 * X^2
Beta  polynomial( 3 )= 0.803273 - 1.42553 * X - 0.543058 * X^2 + 0.362039 * X^3
Beta  polynomial( 4 )= 0.979767 + 1.66538 * X - 1.37575 * X^2 - 0.579262 * X^3 + 0.289631 * X^4
Beta  polynomial( 4 ) roots= [-1.8097,-0.456709,1.45671,2.8097]
Beta  polynomial( 4 ) nodes= [-1.8097,-0.456709,1.45671,2.8097]  and weights= [0.25,0.25,0.25,0.25]
M=
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[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Gamma = class=StandardDistributionPolynomialFactory hasSpecificFamily=false orthonormalization algorithm=class=OrthonormalizationAlgorithm implementation=class=AdaptiveStieltjesAlgorithm measure=class=Gamma name=Gamma dimension=1 k=1 lambda=3 gamma=0 monicRecurrenceCoefficients=[class=Point name=Unnamed dimension=3 values=[1,-0.333333,0],class=Point name=Unnamed dimension=3 values=[1,-1,-0.111111]] monicSquaredNorms=class=Point name=Unnamed dimension=2 values=[1,0.111111] isElliptical=false )
Gamma  polynomial( 0 )= 1
Gamma  polynomial( 1 )= -1 + 3 * X
Gamma  polynomial( 2 )= 1 - 6 * X + 4.5 * X^2
Gamma  polynomial( 3 )= -1 + 9 * X - 13.5 * X^2 + 4.5 * X^3
Gamma  polynomial( 4 )= 1 - 12 * X + 27.0001 * X^2 - 18.0001 * X^3 + 3.37502 * X^4
Gamma  polynomial( 4 ) roots= [0.107516,0.58192,1.51221,3.13169]
Gamma  polynomial( 4 ) nodes= [0.107516,0.58192,1.51221,3.13169]  and weights= [0.603154,0.357419,0.0388879,0.000539296]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
polynomialFactory( Arcsine = class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=ChebychevFactory measure=class=Arcsine name=Arcsine dimension=1 a=-1 b=1 )
Arcsine  polynomial( 0 )= 1
Arcsine  polynomial( 1 )= 1.41421 * X
Arcsine  polynomial( 2 )= -1.41421 + 2.82843 * X^2
Arcsine  polynomial( 3 )= -4.24264 * X + 5.65685 * X^3
Arcsine  polynomial( 4 )= 1.41421 - 11.3137 * X^2 + 11.3137 * X^4
Arcsine  polynomial( 4 ) roots= [-0.92388,-0.382683,0.382683,0.92388]
Arcsine  polynomial( 4 ) nodes= [-0.92388,-0.382683,0.382683,0.92388]  and weights= [0.25,0.25,0.25,0.25]
M=
 5x5
[[ 1 0 0 0 0 ]
 [ 0 1 0 0 0 ]
 [ 0 0 1 0 0 ]
 [ 0 0 0 1 0 ]
 [ 0 0 0 0 1 ]]
