Lamé Functions - 29.6 Fourier Series

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
29.6.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1}
\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..infinity) = 1
 
Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1
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29.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0}
\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(2)*A[0]+ sum(A[2*p], p = 1..infinity) > 0
 
Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0
 Skipped - no semantic math Skipped - no semantic math - -
29.6.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n, \nu = 2n, m > n} 
limit((A[2*p + 2])/(A[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[A, 2*p + 2],Subscript[A, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{p} = 4p^{2}(2-k^{2})}
\beta_{p} = 4p^{2}(2-k^{2})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[p] = 4*(p)^(2)*(2 - (k)^(2))
 
Subscript[\[Beta], p] == 4*(p)^(2)*(2 - (k)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)
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29.6.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1}
\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1 -(1)/(2)*(k)^(2))*((1)/(2)*(C[0])^(2)+ sum((C[2*p])^(2), p = 1..infinity))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..infinity) = 1
 
(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1
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29.6.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0}
\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(2)*C[0]+ sum(C[2*p], p = 1..infinity) > 0
 
Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0
 Skipped - no semantic math Skipped - no semantic math - -
29.6.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+1, \nu = 2n+1, m > n} 
limit((C[2*p + 2])/(C[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[C, 2*p + 2],Subscript[C, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}A_{2p+1}^{2} = 1}
\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((A[2*p + 1])^(2), p = 0..infinity) = 1
 
Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1
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29.6.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}A_{2p+1} > 0}
\sum_{p=0}^{\infty}A_{2p+1} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum(A[2*p + 1], p = 0..infinity) > 0
 
Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+1, \nu = 2n+1, m > n} 
limit((A[2*p + 1])/(A[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[A, 2*p + 1],Subscript[A, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)
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29.6#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)
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29.6.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}C_{2p+1} > 0}
\sum_{p=0}^{\infty}C_{2p+1} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum(C[2*p + 1], p = 0..infinity) > 0
 
Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+2, \nu = 2n+2, m > n} 
limit((C[2*p + 1])/(C[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[C, 2*p + 1],Subscript[C, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6.E35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}B_{2p+1}^{2} = 1}
\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((B[2*p + 1])^(2), p = 0..infinity) = 1
 
Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1
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29.6.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0}
\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((2*p + 1)*B[2*p + 1], p = 0..infinity) > 0
 
Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+1, \nu = 2n+1, m > n} 
limit((B[2*p + 1])/(B[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[B, 2*p + 1],Subscript[B, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.6.E43 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0}
\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((2*p + 1)*D[2*p + 1], p = 0..infinity) > 0
 
Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E44 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+2, \nu = 2n+2, m > n} 
limit((D[2*p + 1])/(D[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[D, 2*p + 1],Subscript[D, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6.E50 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=1}^{\infty}B_{2p}^{2} = 1}
\sum_{p=1}^{\infty}B_{2p}^{2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((B[2*p])^(2), p = 1..infinity) = 1
 
Sum[(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1
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29.6.E51 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0}
\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((2*p + 2)*B[2*p + 2], p = 0..infinity) > 0
 
Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E52 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+2, \nu = 2n+2, m > n} 
limit((B[2*p + 2])/(B[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[B, 2*p + 2],Subscript[B, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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29.6#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)
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29.6#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{p} = (2p+2)^{2}(2-k^{2})}
\beta_{p} = (2p+2)^{2}(2-k^{2})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))
 
Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))
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29.6#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)
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29.6.E57 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1}
\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1 -(1)/(2)*(k)^(2))*sum((D[2*p])^(2), p = 1..infinity)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..infinity) = 1
 
(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1
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29.6.E58 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0}
\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((2*p + 2)*D[2*p + 2], p = 0..infinity) > 0
 
Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0
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29.6.E59 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}}
\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \neq 2n+3, \nu = 2n+3, m > n} 
limit((D[2*p + 2])/(D[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))
 
Limit[Divide[Subscript[D, 2*p + 2],Subscript[D, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]
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