Jacobian Elliptic Functions - 22.15 Inverse Functions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
22.15.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{\xi}{k} = x}
\Jacobiellsnk@{\xi}{k} = x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1} 
JacobiSN(xi, k) = x

JacobiSN[\[Xi], (k)^2] == x
Failure Failure
Failed [30 / 30]
Result: .2924027565+.2435601371*I
Test Values: {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 1}


Result: .1797898601-.1565493762e-1*I
Test Values: {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 2}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[0.29240275641803626, 0.2435601371571337]
Test Values: {Rule[k, 1], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.17978986006074704, -0.015654937469336286]
Test Values: {Rule[k, 2], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.15.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{\eta}{k} = x}
\Jacobiellcnk@{\eta}{k} = x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1} 
JacobiCN(eta, k) = x

JacobiCN[\[Eta], (k)^2] == x
Failure Failure
Failed [30 / 30]
Result: .2107428373-.2715436778*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 1}


Result: .2337173832+.1450431473e-1*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 2}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[0.21074283744314704, -0.27154367778248023]
Test Values: {Rule[k, 1], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.23371738317128377, 0.01450431459800293]
Test Values: {Rule[k, 2], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.15.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{\zeta}{k} = x}
\Jacobielldnk@{\zeta}{k} = x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} \leq x, x \leq 1} 
JacobiDN(InverseJacobiDN(x, k), k) = x

JacobiDN[InverseJacobiDN[x, (k)^2], (k)^2] == x
Successful Successful - Successful [Tested: 1]
22.15.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -K \leq \aJacobiellsnk@{x}{k}}
-K \leq \aJacobiellsnk@{x}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
- EllipticK(k) <= InverseJacobiSN(x, k)

- EllipticK[(k)^2] <= InverseJacobiSN[x, (k)^2]
Failure Failure Error
Failed [9 / 9]
Result: LessEqual[DirectedInfinity[], Complex[0.8047189562170503, -1.5707963267948966]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[Complex[-0.8428751774062981, 1.0782578237498217], Complex[0.372543189356477, -1.0782578237498215]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} \leq K}
\aJacobiellsnk@{x}{k} \leq K		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
InverseJacobiSN(x, k) <= EllipticK(k)

InverseJacobiSN[x, (k)^2] <= EllipticK[(k)^2]
Failure Failure Error
Failed [9 / 9]
Result: LessEqual[Complex[0.8047189562170503, -1.5707963267948966], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[Complex[0.372543189356477, -1.0782578237498215], Complex[0.8428751774062981, -1.0782578237498217]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \aJacobiellcnk@{x}{k}}
0 \leq \aJacobiellcnk@{x}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
0 <= InverseJacobiCN(x, k)

0 <= InverseJacobiCN[x, (k)^2]
Failure Failure Successful [Tested: 9]
Failed [8 / 9]
Result: LessEqual[0.0, Complex[0.0, 0.8410686705679303]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[0.0, Complex[5.551115123125783*^-16, 0.6872864564092609]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} \leq 2K}
\aJacobiellcnk@{x}{k} \leq 2K		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
InverseJacobiCN(x, k) <= 2*EllipticK(k)

InverseJacobiCN[x, (k)^2] <= 2*EllipticK[(k)^2]
Failure Failure Error
Failed [9 / 9]
Result: LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[Complex[5.551115123125783*^-16, 0.6872864564092609], Complex[1.6857503548125963, -2.1565156474996434]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \aJacobielldnk@{x}{k}}
0 \leq \aJacobielldnk@{x}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
0 <= InverseJacobiDN(x, k)

0 <= InverseJacobiDN[x, (k)^2]
Failure Failure Successful [Tested: 9]
Failed [8 / 9]
Result: LessEqual[0.0, Complex[0.0, 0.8410686705679303]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[0.0, Complex[1.6857503548125963, -1.6950867772240739]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} \leq K}
\aJacobielldnk@{x}{k} \leq K		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
InverseJacobiDN(x, k) <= EllipticK(k)

InverseJacobiDN[x, (k)^2] <= EllipticK[(k)^2]
Failure Failure Error
Failed [9 / 9]
Result: LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}


Result: LessEqual[Complex[1.6857503548125963, -1.6950867772240739], Complex[0.8428751774062981, -1.0782578237498217]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = (-1)^{m}\aJacobiellsnk@{x}{k}+2mK}
\xi = (-1)^{m}\aJacobiellsnk@{x}{k}+2mK		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
xi = (- 1)^(m)* InverseJacobiSN(x, k)+ 2*m*K

\[Xi] == (- 1)^(m)* InverseJacobiSN[x, (k)^2]+ 2*m*K
Failure Failure
Failed [300 / 300]
Result: -.613064478e-1-2.070796327*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 1}


Result: -3.402795168+.70796327e-1*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.061306447567388456, -2.0707963267948966]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-3.4027951675703663, 0.07079632679489672]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.15.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = +\aJacobiellcnk@{x}{k}+4mK}
\eta = +\aJacobiellcnk@{x}{k}+4mK		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
eta = + InverseJacobiCN(x, k)+ 4*m*K

\[Eta] == + InverseJacobiCN[x, (k)^2]+ 4*m*K
Failure Failure
Failed [300 / 300]
Result: -2.598076212-2.341068671*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}


Result: -6.062177828-4.341068671*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-2.598076211353316, -2.34106867056793]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-6.062177826491071, -4.34106867056793]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.15.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = -\aJacobiellcnk@{x}{k}+4mK}
\eta = -\aJacobiellcnk@{x}{k}+4mK		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
eta = - InverseJacobiCN(x, k)+ 4*m*K

\[Eta] == - InverseJacobiCN[x, (k)^2]+ 4*m*K
Failure Failure
Failed [300 / 300]
Result: -2.598076212-.6589313294*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}


Result: -6.062177828-2.658931329*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-2.598076211353316, -0.6589313294320696]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-6.062177826491071, -2.658931329432069]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.15.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = +\aJacobielldnk@{x}{k}+2mK}
\zeta = +\aJacobielldnk@{x}{k}+2mK		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(InverseJacobiDN(x, k)) = + InverseJacobiDN(x, k)+ 2*m*K

(InverseJacobiDN[x, (k)^2]) == + InverseJacobiDN[x, (k)^2]+ 2*m*K
Failure Failure
Failed [270 / 270]
Result: -1.732050808-1.000000000*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}


Result: -3.464101616-2.*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}

... skip entries to safe data
Failed [270 / 270]
Result: Complex[-1.7320508075688774, -0.9999999999999999]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}


Result: Complex[-3.464101615137755, -1.9999999999999998]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = -\aJacobielldnk@{x}{k}+2mK}
\zeta = -\aJacobielldnk@{x}{k}+2mK		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(InverseJacobiDN(x, k)) = - InverseJacobiDN(x, k)+ 2*m*K

(InverseJacobiDN[x, (k)^2]) == - InverseJacobiDN[x, (k)^2]+ 2*m*K
Failure Failure
Failed [270 / 270]
Result: -1.732050808+.682137341*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}


Result: -3.464101616-.317862659*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}

... skip entries to safe data
Failed [270 / 270]
Result: Complex[-1.7320508075688774, 0.6821373411358608]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}


Result: Complex[-3.464101615137755, -0.3178626588641391]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]}

... skip entries to safe data
22.15.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \int_{0}^{\Jacobiellsnk@{x}{k}}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}}
x = \int_{0}^{\Jacobiellsnk@{x}{k}}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1, 0 \leq k, k \leq 1} 
x = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..JacobiSN(x, k))

x == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, JacobiSN[x, (k)^2]}, GenerateConditions->None]
Failure Aborted Successful [Tested: 1] Skipped - Because timed out
22.15.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}}
\aJacobiellsnk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1} 
InverseJacobiSN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..x)

InverseJacobiSN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None]
Error Aborted - Skipped - Because timed out
22.15.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}}}
\aJacobiellcnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1} 
InverseJacobiCN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2)))), t = x..1)

InverseJacobiCN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None]
Error Aborted - Skipped - Because timed out
22.15.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}}}
\aJacobielldnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} \leq x, x \leq 1} 
InverseJacobiDN(x, k) = int((1)/(sqrt((1 - (t)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..1)

InverseJacobiDN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, 1}, GenerateConditions->None]
Error Aborted - Skipped - Because timed out
22.15.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcdk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}}
\aJacobiellcdk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1} 
InverseJacobiCD(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = x..1)

InverseJacobiCD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None]
Failure Aborted Error Skipped - Because timed out
22.15.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsdk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}}}
\aJacobiellsdk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1/k^{\prime} \leq x, x \leq 1/k^{\prime}} 
InverseJacobiSD(x, k) = int((1)/(sqrt((1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2)))), t = 0..x)

InverseJacobiSD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None]
Error Failure - Skip - No test values generated
22.15.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellndk@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(1-{k^{\prime}}^{2}t^{2})}}}
\aJacobiellndk@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(1-{k^{\prime}}^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq x, x \leq 1/k^{\prime}} 
InverseJacobiND(x, k) = int((1)/(sqrt(((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2)))), t = 1..x)
 
InverseJacobiND[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None]
 Error Failure - Skip - No test values generated
22.15.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}}
\aJacobielldck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq x, x < \infty} 
InverseJacobiDC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = 1..x)
 
InverseJacobiDC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, 1, x}, GenerateConditions->None]
 Failure Aborted Error Skipped - Because timed out
22.15.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}}}
\aJacobiellnck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq x, x < \infty} 
InverseJacobiNC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2)))), t = 1..x)
 
InverseJacobiNC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None]
 Failure Aborted Skipped - Because timed out Skipped - Because timed out
22.15.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsck@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}}}
\aJacobiellsck@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\infty < x, x < \infty} 
InverseJacobiSC(x, k) = int((1)/(sqrt((1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2)))), t = 0..x)
 
InverseJacobiSC[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2))]], {t, 0, x}, GenerateConditions->None]
 Error Aborted - Skipped - Because timed out
22.15.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}}
\aJacobiellnsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq x, x < \infty} 
InverseJacobiNS(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = x..infinity)
 
InverseJacobiNS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]
 Failure Aborted Skipped - Because timed out Skipped - Because timed out
22.15.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}}}
\aJacobielldsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} \leq x, x < \infty} 
InverseJacobiDS(x, k) = int((1)/(sqrt(((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..infinity)
 
InverseJacobiDS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]
 Error Aborted - Skipped - Because timed out
22.15.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}}}
\aJacobiellcsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\infty < x, x < \infty} 
InverseJacobiCS(x, k) = int((1)/(sqrt((1 + (t)^(2))*((t)^(2)+1 - (k)^(2)))), t = x..infinity)
 
InverseJacobiCS[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*((t)^(2)+1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]
 Error Aborted - Skipped - Because timed out
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