Jacobian Elliptic Functions - 22.18 Mathematical Applications

From testwiki
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
22.18.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right) = 1}
\left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right) = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) = 1
 
((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) == 1
 Skipped - no semantic math Skipped - no semantic math - -
22.18#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\Jacobiellsnk@{u}{k}}
x = a\Jacobiellsnk@{u}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x = a*JacobiSN(u, k)

x == a*JacobiSN[u, (k)^2]
Failure Failure
Failed [300 / 300]
Result: 2.688604135+.3653402056*I
Test Values: {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}


Result: 2.519684790-.2348240643e-1*I
Test Values: {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[2.688604134627054, 0.3653402057357006]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}


Result: Complex[2.5196847900911203, -0.02348240620400443]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}

... skip entries to safe data
22.18#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\Jacobiellcnk@{u}{k}}
y = b\Jacobiellcnk@{u}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
y = b*JacobiCN(u, k)

y == b*JacobiCN[u, (k)^2]
Failure Failure
Failed [300 / 300]
Result: -.433885744-.4073155167*I
Test Values: {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1}


Result: -.399423925+.2175647210e-1*I
Test Values: {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.43388574383527945, -0.40731551667372035]
Test Values: {Rule[b, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}


Result: Complex[-0.39942392524307424, 0.021756471897004394]
Test Values: {Rule[b, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}

... skip entries to safe data
22.18.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}}
l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
l(r) = (1/(sqrt(2)))*InverseJacobiCN(r, 1/(sqrt(2)))

l[r] == (1/(Sqrt[2]))*InverseJacobiCN[r, (1/(Sqrt[2]))^2]
Failure Failure
Failed [18 / 18]
Result: -4.122057553+.6299669258*I
Test Values: {r = -3/2, l = 1}


Result: -5.622057553+.6299669258*I
Test Values: {r = -3/2, l = 2}

... skip entries to safe data
Failed [18 / 18]
Result: Complex[-4.12205755429212, 0.629966925905157]
Test Values: {Rule[l, 1], Rule[r, -1.5]}


Result: Complex[-5.62205755429212, 0.629966925905157]
Test Values: {Rule[l, 2], Rule[r, -1.5]}

... skip entries to safe data
22.18.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}}
r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
r = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))

r == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]
Failure Failure
Failed [18 / 18]
Result: -1.810737930
Test Values: {r = -3/2, l = 1}


Result: -.8262668012
Test Values: {r = -3/2, l = 2}

... skip entries to safe data
Failed [18 / 18]
Result: -1.810737930333856
Test Values: {Rule[l, 1], Rule[r, -1.5]}


Result: -0.8262668010254658
Test Values: {Rule[l, 2], Rule[r, -1.5]}

... skip entries to safe data
22.18#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}}
x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))*JacobiDN(sqrt(2)*l, 1/(sqrt(2)))

x == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]*JacobiDN[Sqrt[2]*l, (1/(Sqrt[2]))^2]
Failure Failure
Failed [9 / 9]
Result: 1.269911408
Test Values: {x = 3/2, l = 1}


Result: 2.074437352
Test Values: {x = 3/2, l = 2}

... skip entries to safe data
Failed [9 / 9]
Result: 1.2699114077583538
Test Values: {Rule[l, 1], Rule[x, 1.5]}


Result: 2.0744373520381156
Test Values: {Rule[l, 2], Rule[x, 1.5]}

... skip entries to safe data
22.18.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f = 0}
ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + exp(1)*(x + y)+ f = 0
 
a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + E*(x + y)+ f == 0
 Skipped - no semantic math Skipped - no semantic math - -
22.18#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{3} = \frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}}
x_{3} = \frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x[3] = (x[1]*y[2]+ x[2]*y[1])/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))
 
Subscript[x, 3] == Divide[Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1],1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]
 Skipped - no semantic math Skipped - no semantic math - -
22.18#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{3} = \frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}}
y_{3} = \frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
y[3] = (y[1]*y[2]+ x[2]*(-(1 + (k)^(2))*x[1]+ 2*(k)^(2)* (x[1])^(3)))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))+ x[3]*(2*(k)^(2)* x[1]*y[1]*(x[2])^(2))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))
 
Subscript[y, 3] == Divide[Subscript[y, 1]*Subscript[y, 2]+ Subscript[x, 2]*(-(1 + (k)^(2))*Subscript[x, 1]+ 2*(k)^(2)* (Subscript[x, 1])^(3)),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]+ Subscript[x, 3]*Divide[2*(k)^(2)* Subscript[x, 1]*Subscript[y, 1]*(Subscript[x, 2])^(2),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]
 Skipped - no semantic math Skipped - no semantic math - -
Retrieved from "https://lct.wmflabs.org/w/index.php?title=22.18&oldid=58417"