33.19: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.19.E4 33.19.E4] || [[Item:Q9662|<math>\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[k]- gamma[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*gamma[k - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], k]- Subscript[\[Gamma], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.19.E4 33.19.E4] || <math qid="Q9662">\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[k]- gamma[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*gamma[k - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], k]- Subscript[\[Gamma], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.19.E6 33.19.E6] || [[Item:Q9665|<math>k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">k*(k + 2*ell + 1)*delta[k]+ 2*delta[k - 1]+ epsilon*delta[k - 2]+ 2*(2*k + 2*ell + 1)*(product(1 + epsilon*(k)^(2), k = 0..ell))*alpha[k] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">k*(k + 2*\[ScriptL]+ 1)*Subscript[\[Delta], k]+ 2*Subscript[\[Delta], k - 1]+ \[Epsilon]*Subscript[\[Delta], k - 2]+ 2*(2*k + 2*\[ScriptL]+ 1)*(Product[1 + \[Epsilon]*(k)^(2), {k, 0, \[ScriptL]}, GenerateConditions->None])*Subscript[\[Alpha], k] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.19.E6 33.19.E6] || <math qid="Q9665">k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">k*(k + 2*ell + 1)*delta[k]+ 2*delta[k - 1]+ epsilon*delta[k - 2]+ 2*(2*k + 2*ell + 1)*(product(1 + epsilon*(k)^(2), k = 0..ell))*alpha[k] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">k*(k + 2*\[ScriptL]+ 1)*Subscript[\[Delta], k]+ 2*Subscript[\[Delta], k - 1]+ \[Epsilon]*Subscript[\[Delta], k - 2]+ 2*(2*k + 2*\[ScriptL]+ 1)*(Product[1 + \[Epsilon]*(k)^(2), {k, 0, \[ScriptL]}, GenerateConditions->None])*Subscript[\[Alpha], k] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/33.19.E7 33.19.E7] || [[Item:Q9666|<math>\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[k]- beta[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*beta[k - 2]+(1)/(2)*(k - 1)*epsilon*gamma[k - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], k]- Subscript[\[Beta], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Beta], k - 2]+Divide[1,2]*(k - 1)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.19.E7 33.19.E7] || <math qid="Q9666">\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[k]- beta[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*beta[k - 2]+(1)/(2)*(k - 1)*epsilon*gamma[k - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], k]- Subscript[\[Beta], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Beta], k - 2]+Divide[1,2]*(k - 1)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 12:14, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
33.19.E4 γ k - γ k - 1 + 1 4 ⁢ ( k - 1 ) ⁢ ( k - 2 ⁢ ℓ - 2 ) ⁢ ϵ ⁢ γ k - 2 = 0 subscript 𝛾 𝑘 subscript 𝛾 𝑘 1 1 4 𝑘 1 𝑘 2 ℓ 2 italic-ϵ subscript 𝛾 𝑘 2 0 {\displaystyle{\displaystyle\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-% 2)\epsilon\gamma_{k-2}=0}}
\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0		 

gamma[k]- gamma[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*gamma[k - 2] = 0
 
Subscript[\[Gamma], k]- Subscript[\[Gamma], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0
 Skipped - no semantic math Skipped - no semantic math - -
33.19.E6 k ⁢ ( k + 2 ⁢ ℓ + 1 ) ⁢ δ k + 2 ⁢ δ k - 1 + ϵ ⁢ δ k - 2 + 2 ⁢ ( 2 ⁢ k + 2 ⁢ ℓ + 1 ) ⁢ A ⁢ ( ϵ , ℓ ) ⁢ α k = 0 𝑘 𝑘 2 ℓ 1 subscript 𝛿 𝑘 2 subscript 𝛿 𝑘 1 italic-ϵ subscript 𝛿 𝑘 2 2 2 𝑘 2 ℓ 1 𝐴 italic-ϵ ℓ subscript 𝛼 𝑘 0 {\displaystyle{\displaystyle k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon% \delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k}=0}}
k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0		 

k*(k + 2*ell + 1)*delta[k]+ 2*delta[k - 1]+ epsilon*delta[k - 2]+ 2*(2*k + 2*ell + 1)*(product(1 + epsilon*(k)^(2), k = 0..ell))*alpha[k] = 0
 
k*(k + 2*\[ScriptL]+ 1)*Subscript[\[Delta], k]+ 2*Subscript[\[Delta], k - 1]+ \[Epsilon]*Subscript[\[Delta], k - 2]+ 2*(2*k + 2*\[ScriptL]+ 1)*(Product[1 + \[Epsilon]*(k)^(2), {k, 0, \[ScriptL]}, GenerateConditions->None])*Subscript[\[Alpha], k] == 0
 Skipped - no semantic math Skipped - no semantic math - -
33.19.E7 β k - β k - 1 + 1 4 ⁢ ( k - 1 ) ⁢ ( k - 2 ⁢ ℓ - 2 ) ⁢ ϵ ⁢ β k - 2 + 1 2 ⁢ ( k - 1 ) ⁢ ϵ ⁢ γ k - 2 = 0 subscript 𝛽 𝑘 subscript 𝛽 𝑘 1 1 4 𝑘 1 𝑘 2 ℓ 2 italic-ϵ subscript 𝛽 𝑘 2 1 2 𝑘 1 italic-ϵ subscript 𝛾 𝑘 2 0 {\displaystyle{\displaystyle\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)% \epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2}=0}}
\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0		 

beta[k]- beta[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*beta[k - 2]+(1)/(2)*(k - 1)*epsilon*gamma[k - 2] = 0
 
Subscript[\[Beta], k]- Subscript[\[Beta], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Beta], k - 2]+Divide[1,2]*(k - 1)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0
 Skipped - no semantic math Skipped - no semantic math - -
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