Lamé Functions - 29.15 Fourier Series and Chebyshev Series
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 29.15.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}^{n}A_{2p}^{2} = 1}
\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}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..n) = 1 |
Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, n}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.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}^{n}A_{2p} > 0}
\tfrac{1}{2}A_{0}+\sum_{p=1}^{n}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..n) > 0 |
Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}A_{2p+1}^{2} = 1}
\sum_{p=0}^{n}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..n) = 1 |
Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}A_{2p+1} > 0}
\sum_{p=0}^{n}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..n) > 0 |
Sum[Subscript[A, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}B_{2p+1}^{2} = 1}
\sum_{p=0}^{n}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..n) = 1 |
Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+1)B_{2p+1} > 0}
\sum_{p=0}^{n}(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..n) > 0 |
Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E20 | 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}^{n}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{n-1}C_{2p}C_{2p+2} = 1}
\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{n}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{n-1}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..n))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..n - 1) = 1 |
(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, n}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, n - 1}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0}
\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}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..n) > 0 |
Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}B_{2p+2}^{2} = 1}
\sum_{p=0}^{n}B_{2p+2}^{2} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((B[2*p + 2])^(2), p = 0..n) = 1 |
Sum[(Subscript[B, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+2)B_{2p+2} > 0}
\sum_{p=0}^{n}(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..n) > 0 |
Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}C_{2p+1} > 0}
\sum_{p=0}^{n}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..n) > 0 |
Sum[Subscript[C, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+1)D_{2p+1} > 0}
\sum_{p=0}^{n}(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..n) > 0 |
Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E40 | 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=0}^{n}D_{2p+2}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{n}D_{2p}D_{2p+2} = 1}
\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=0}^{n}D_{2p+2}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{n}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])^(2), p = 0..n)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..n) = 1 |
(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, n}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.15.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+2)D_{2p+2} > 0}
\sum_{p=0}^{n}(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..n) > 0 |
Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |