View source for 29.15

{{DISPLAYTITLE:Lamé Functions - 29.15 Fourier Series and Chebyshev Series}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/29.15.E5 29.15.E5] || [[Item:Q8750|<math>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}A_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}A_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E6 29.15.E6] || [[Item:Q8751|<math>\tfrac{1}{2}A_{0}+\sum_{p=1}^{n}A_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}+\sum_{p=1}^{n}A_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*A[0]+ sum(A[2*p], p = 1..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E10 29.15.E10] || [[Item:Q8755|<math>\sum_{p=0}^{n}A_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}A_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((A[2*p + 1])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E11 29.15.E11] || [[Item:Q8756|<math>\sum_{p=0}^{n}A_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}A_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(A[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[A, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E15 29.15.E15] || [[Item:Q8760|<math>\sum_{p=0}^{n}B_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}B_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 1])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E16 29.15.E16] || [[Item:Q8761|<math>\sum_{p=0}^{n}(2p+1)B_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+1)B_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*B[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E20 29.15.E20] || [[Item:Q8765|<math>\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</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\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</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E21 29.15.E21] || [[Item:Q8766|<math>\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*C[0]+ sum(C[2*p], p = 1..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E25 29.15.E25] || [[Item:Q8770|<math>\sum_{p=0}^{n}B_{2p+2}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}B_{2p+2}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 2])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E26 29.15.E26] || [[Item:Q8771|<math>\sum_{p=0}^{n}(2p+2)B_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+2)B_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*B[2*p + 2], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E31 29.15.E31] || [[Item:Q8776|<math>\sum_{p=0}^{n}C_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}C_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(C[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[C, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E36 29.15.E36] || [[Item:Q8781|<math>\sum_{p=0}^{n}(2p+1)D_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+1)D_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*D[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E40 29.15.E40] || [[Item:Q8785|<math>\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</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\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</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/29.15.E41 29.15.E41] || [[Item:Q8786|<math>\sum_{p=0}^{n}(2p+2)D_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+2)D_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*D[2*p + 2], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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