Mathieu Functions and Hill’s Equation - 28.31 Equations of Whittaker–Hill and Ince

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
28.31#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi^{2} = -4k^{2}c^{2}}
\xi^{2} = -4k^{2}c^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(xi)^(2) = - 4*(k)^(2)* (c)^(2)
 
\[Xi]^(2) == - 4*(k)^(2)* (c)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A = \eta-\tfrac{1}{8}\xi^{2}}
A = \eta-\tfrac{1}{8}\xi^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
A = eta -(1)/(8)*(xi)^(2)
 
A == \[Eta]-Divide[1,8]*\[Xi]^(2)
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B = -(p+1)\xi}
B = -(p+1)\xi		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
B = -(p + 1)*xi
 
B == -(p + 1)*\[Xi]
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(z) = w(z)\exp@{-\tfrac{1}{4}\xi\cos@{2z}}}
W(z) = w(z)\exp@{-\tfrac{1}{4}\xi\cos@{2z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
W(z) = w(z)* exp(-(1)/(4)*xi*cos(2*z))

W[z] == w[z]* Exp[-Divide[1,4]*\[Xi]*Cos[2*z]]
Failure Failure
Failed [300 / 300]
Result: .2817275679-.201842736e-1*I
Test Values: {W = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: -.5394015055-.3903737220*I
Test Values: {W = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.2817275677812313, -0.02018427332482242]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.06489049435577782, 0.2500000224743827]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
28.31.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{\mathit{e},s}(z) = \sum_{\ell=0}^{\infty}A_{2\ell+s}\cos@@{(2\ell+s)z}}
w_{\mathit{e},s}(z) = \sum_{\ell=0}^{\infty}A_{2\ell+s}\cos@@{(2\ell+s)z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w[e , s](z) = sum(A[2*ell + s]*cos((2*ell + s)*z), ell = 0..infinity)

Subscript[w, e , s][z] == Sum[Subscript[A, 2*\[ScriptL]+ s]*Cos[(2*\[ScriptL]+ s)*z], {\[ScriptL], 0, Infinity}, GenerateConditions->None]
Error Failure - Skip - No test values generated
28.31.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{\mathit{o},s}(z) = \sum_{\ell=0}^{\infty}B_{2\ell+s}\sin@@{(2\ell+s)z}}
w_{\mathit{o},s}(z) = \sum_{\ell=0}^{\infty}B_{2\ell+s}\sin@@{(2\ell+s)z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w[o , s](z) = sum(B[2*ell + s]*sin((2*ell + s)*z), ell = 0..infinity)

Subscript[w, o , s][z] == Sum[Subscript[B, 2*\[ScriptL]+ s]*Sin[(2*\[ScriptL]+ s)*z], {\[ScriptL], 0, Infinity}, GenerateConditions->None]
Error Failure - Skip - No test values generated
28.31#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2\eta A_{0}+(2+p)\xi A_{2} = 0}
-2\eta A_{0}+(2+p)\xi A_{2} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
- 2*eta*A[0]+(2 + p)*xi*A[2] = 0
 
- 2*\[Eta]*Subscript[A, 0]+(2 + p)*\[Xi]*Subscript[A, 2] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p\xi A_{0}+(4-\eta)A_{2}+\left(\tfrac{1}{2}p+2\right)\xi A_{4} = 0}
p\xi A_{0}+(4-\eta)A_{2}+\left(\tfrac{1}{2}p+2\right)\xi A_{4} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
p*xi*A[0]+(4 - eta)*A[2]+((1)/(2)*p + 2)*xi*A[4] = 0
 
p*\[Xi]*Subscript[A, 0]+(4 - \[Eta])*Subscript[A, 2]+(Divide[1,2]*p + 2)*\[Xi]*Subscript[A, 4] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}p-\ell+1)\xi A_{2\ell-2}+\left(4\ell^{2}-\eta\right)A_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi A_{2\ell+2} = 0}
(\tfrac{1}{2}p-\ell+1)\xi A_{2\ell-2}+\left(4\ell^{2}-\eta\right)A_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi A_{2\ell+2} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell \geq 2} 
((1)/(2)*p - ell + 1)*xi*A[2*ell - 2]+(4*(ell)^(2)- eta)*A[2*ell]+((1)/(2)*p + ell + 1)*xi*A[2*ell + 2] = 0
 
(Divide[1,2]*p - \[ScriptL]+ 1)*\[Xi]*Subscript[A, 2*\[ScriptL]- 2]+(4*\[ScriptL]^(2)- \[Eta])*Subscript[A, 2*\[ScriptL]]+(Divide[1,2]*p + \[ScriptL]+ 1)*\[Xi]*Subscript[A, 2*\[ScriptL]+ 2] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\eta+\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)A_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi A_{3} = 0}
\left(1-\eta+\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)A_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi A_{3} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1 - eta +((1)/(2)*p +(1)/(2))*xi)*A[1]+((1)/(2)*p +(3)/(2))*xi*A[3] = 0
 
(1 - \[Eta]+(Divide[1,2]*p +Divide[1,2])*\[Xi])*Subscript[A, 1]+(Divide[1,2]*p +Divide[3,2])*\[Xi]*Subscript[A, 3] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi A_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)A_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi A_{2\ell+3} = 0}
(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi A_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)A_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi A_{2\ell+3} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell \geq 1} 
((1)/(2)*p - ell +(1)/(2))*xi*A[2*ell - 1]+((2*ell + 1)^(2)- eta)*A[2*ell + 1]+((1)/(2)*p + ell +(3)/(2))*xi*A[2*ell + 3] = 0
 
(Divide[1,2]*p - \[ScriptL]+Divide[1,2])*\[Xi]*Subscript[A, 2*\[ScriptL]- 1]+((2*\[ScriptL]+ 1)^(2)- \[Eta])*Subscript[A, 2*\[ScriptL]+ 1]+(Divide[1,2]*p + \[ScriptL]+Divide[3,2])*\[Xi]*Subscript[A, 2*\[ScriptL]+ 3] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\eta-\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)B_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi B_{3} = 0}
\left(1-\eta-\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)B_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi B_{3} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1 - eta -((1)/(2)*p +(1)/(2))*xi)*B[1]+((1)/(2)*p +(3)/(2))*xi*B[3] = 0
 
(1 - \[Eta]-(Divide[1,2]*p +Divide[1,2])*\[Xi])*Subscript[B, 1]+(Divide[1,2]*p +Divide[3,2])*\[Xi]*Subscript[B, 3] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi B_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)B_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi B_{2\ell+3} = 0}
(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi B_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)B_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi B_{2\ell+3} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell \geq 1} 
((1)/(2)*p - ell +(1)/(2))*xi*B[2*ell - 1]+((2*ell + 1)^(2)- eta)*B[2*ell + 1]+((1)/(2)*p + ell +(3)/(2))*xi*B[2*ell + 3] = 0
 
(Divide[1,2]*p - \[ScriptL]+Divide[1,2])*\[Xi]*Subscript[B, 2*\[ScriptL]- 1]+((2*\[ScriptL]+ 1)^(2)- \[Eta])*Subscript[B, 2*\[ScriptL]+ 1]+(Divide[1,2]*p + \[ScriptL]+Divide[3,2])*\[Xi]*Subscript[B, 2*\[ScriptL]+ 3] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (4-\eta)B_{2}+\left(\tfrac{1}{2}p+2\right)\xi B_{4} = 0}
(4-\eta)B_{2}+\left(\tfrac{1}{2}p+2\right)\xi B_{4} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(4 - eta)*B[2]+((1)/(2)*p + 2)*xi*B[4] = 0
 
(4 - \[Eta])*Subscript[B, 2]+(Divide[1,2]*p + 2)*\[Xi]*Subscript[B, 4] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}p-\ell+1)\xi B_{2\ell-2}+(4\ell^{2}-\eta)B_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi B_{2\ell+2} = 0}
(\tfrac{1}{2}p-\ell+1)\xi B_{2\ell-2}+(4\ell^{2}-\eta)B_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi B_{2\ell+2} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell \geq 2} 
((1)/(2)*p - ell + 1)*xi*B[2*ell - 2]+(4*(ell)^(2)- eta)*B[2*ell]+((1)/(2)*p + ell + 1)*xi*B[2*ell + 2] = 0
 
(Divide[1,2]*p - \[ScriptL]+ 1)*\[Xi]*Subscript[B, 2*\[ScriptL]- 2]+(4*\[ScriptL]^(2)- \[Eta])*Subscript[B, 2*\[ScriptL]]+(Divide[1,2]*p + \[ScriptL]+ 1)*\[Xi]*Subscript[B, 2*\[ScriptL]+ 2] == 0
 Skipped - no semantic math Skipped - no semantic math - -
28.31.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\diff{x} = \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x}}
\dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\diff{x} = \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(Pi)*int(((C[p])^(m)(x , xi))^(2), x = 0..2*Pi) = (1)/(Pi)*int(((S[p])^(m)(x , xi))^(2), x = 0..2*Pi)

Divide[1,Pi]*Integrate[((Subscript[C, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[((Subscript[S, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None]
Failure Failure Error Error
28.31.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x} = 1}
\dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(Pi)*int(((S[p])^(m)(x , xi))^(2), x = 0..2*Pi) = 1

Divide[1,Pi]*Integrate[((Subscript[S, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == 1
Failure Failure Error Error
28.31#Ex22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathit{hc}_{2n}^{2m}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n}^{2m}(\tfrac{1}{2}\pi-z,\xi)}
\mathit{hc}_{2n}^{2m}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n}^{2m}(\tfrac{1}{2}\pi-z,\xi)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(hc[2*n])^(2*m)(z , - xi) = (- 1)^(m)* (hc[2*n])^(2*m)((1)/(2)*Pi - z , xi)
 
(Subscript[hc, 2*n])^(2*m)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hc, 2*n])^(2*m)[Divide[1,2]*Pi - z , \[Xi]]
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathit{hc}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)}
\mathit{hc}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(hc[2*n + 1])^(2*m + 1)(z , - xi) = (- 1)^(m)* (hs[2*n + 1])^(2*m + 1)((1)/(2)*Pi - z , xi)
 
(Subscript[hc, 2*n + 1])^(2*m + 1)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hs, 2*n + 1])^(2*m + 1)[Divide[1,2]*Pi - z , \[Xi]]
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathit{hs}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)}
\mathit{hs}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(hs[2*n + 1])^(2*m + 1)(z , - xi) = (- 1)^(m)* (hc[2*n + 1])^(2*m + 1)((1)/(2)*Pi - z , xi)
 
(Subscript[hs, 2*n + 1])^(2*m + 1)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hc, 2*n + 1])^(2*m + 1)[Divide[1,2]*Pi - z , \[Xi]]
 Skipped - no semantic math Skipped - no semantic math - -
28.31#Ex25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathit{hs}_{2n+2}^{2m+2}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+2}^{2m+2}(\tfrac{1}{2}\pi-z,\xi)}
\mathit{hs}_{2n+2}^{2m+2}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+2}^{2m+2}(\tfrac{1}{2}\pi-z,\xi)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(hs[2*n + 2])^(2*m + 2)(z , - xi) = (- 1)^(m)* (hs[2*n + 2])^(2*m + 2)((1)/(2)*Pi - z , xi)
 
(Subscript[hs, 2*n + 2])^(2*m + 2)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hs, 2*n + 2])^(2*m + 2)[Divide[1,2]*Pi - z , \[Xi]]
 Skipped - no semantic math Skipped - no semantic math - -
28.31.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\mathit{hc}_{p}^{m_{1}}(x,\xi)\mathit{hc}_{p}^{m_{2}}(x,\xi)\diff{x} = \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x}}
\int_{0}^{2\pi}\mathit{hc}_{p}^{m_{1}}(x,\xi)\mathit{hc}_{p}^{m_{2}}(x,\xi)\diff{x} = \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int((hc[p])^(m[1])(x , xi)* (hc[p])^(m[2])(x , xi), x = 0..2*Pi) = int((hs[p])^(m[1])(x , xi)* (hs[p])^(m[2])(x , xi), x = 0..2*Pi)

Integrate[(Subscript[hc, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hc, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None] == Integrate[(Subscript[hs, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hs, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None]
Failure Failure Manual Skip! Error
28.31.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x} = 0}
\int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int((hs[p])^(m[1])(x , xi)* (hs[p])^(m[2])(x , xi), x = 0..2*Pi) = 0

Integrate[(Subscript[hs, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hs, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None] == 0
Failure Failure Manual Skip! Error
28.31.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0}
\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int(int((hc[p[1]])^(m[1])(u , xi)* (hc[p[1]])^(m[1])(v , xi)* (hc[p[2]])^(m[2])(u , xi)* (hc[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0

Integrate[Integrate[(Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hc, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hc, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0
Failure Failure Error Error
28.31.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0}
\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int(int((hs[p[1]])^(m[1])(u , xi)* (hs[p[1]])^(m[1])(v , xi)* (hs[p[2]])^(m[2])(u , xi)* (hs[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0

Integrate[Integrate[(Subscript[hs, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hs, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0
Failure Failure Error Error
28.31.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0}
\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int(int((hc[p[1]])^(m[1])(u , xi)* (hc[p[1]])^(m[1])(v , xi)* (hs[p[2]])^(m[2])(u , xi)* (hs[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0

Integrate[Integrate[(Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0
Failure Failure Error Error
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