33.5: 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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| [https://dlmf.nist.gov/33.5#Ex7 33.5#Ex7] || [[Item:Q9523|<math>\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</syntaxhighlight> || <math>\realpart@@{((\ell+\frac{1}{2})+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| [https://dlmf.nist.gov/33.5#Ex7 33.5#Ex7] || <math qid="Q9523">\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</syntaxhighlight> || <math>\realpart@@{((\ell+\frac{1}{2})+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
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| [https://dlmf.nist.gov/33.5#Ex9 33.5#Ex9] || [[Item:Q9525|<math>\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CoulombF(0, 0, rho) = sin(rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| [https://dlmf.nist.gov/33.5#Ex9 33.5#Ex9] || <math qid="Q9525">\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CoulombF(0, 0, rho) = sin(rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/33.5.E6 33.5.E6] || [[Item:Q9528|<math>\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</syntaxhighlight> || <math>\realpart@@{(\ell+1+\iunit\eta)} > 0</math> || <syntaxhighlight lang=mathematica>((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]]
| [https://dlmf.nist.gov/33.5.E6 33.5.E6] || <math qid="Q9528">\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</syntaxhighlight> || <math>\realpart@@{(\ell+1+\iunit\eta)} > 0</math> || <syntaxhighlight lang=mathematica>((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]]
Test Values: {}</syntaxhighlight><br></div></div>
Test Values: {}</syntaxhighlight><br></div></div>
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Latest revision as of 12:13, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
33.5#Ex7 F ℓ ⁡ ( 0 , ρ ) = ( π ⁢ ρ / 2 ) 1 / 2 ⁢ J ℓ + 1 2 ⁡ ( ρ ) regular-Coulomb-F ℓ 0 𝜌 superscript 𝜋 𝜌 2 1 2 Bessel-J ℓ 1 2 𝜌 {\displaystyle{\displaystyle F_{\ell}\left(0,\rho\right)=(\pi\rho/2)^{1/2}J_{% \ell+\frac{1}{2}}\left(\rho\right)}}
\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}		 ℜ ⁡ ( ( ℓ + 1 2 ) + k + 1 ) > 0 ℓ 1 2 𝑘 1 0 {\displaystyle{\displaystyle\Re((\ell+\frac{1}{2})+k+1)>0}} 
CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)

Error
Failure Missing Macro Error Error -
33.5#Ex9 F 0 ⁡ ( 0 , ρ ) = sin ⁡ ρ regular-Coulomb-F 0 0 𝜌 𝜌 {\displaystyle{\displaystyle F_{0}\left(0,\rho\right)=\sin\rho}}
\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}		 

CoulombF(0, 0, rho) = sin(rho)

Error
Successful Missing Macro Error - -
33.5.E6 2 ℓ ⁢ ℓ ! ( 2 ⁢ ℓ + 1 ) ! = 1 ( 2 ⁢ ℓ + 1 ) !! superscript 2 ℓ ℓ 2 ℓ 1 1 double-factorial 2 ℓ 1 {\displaystyle{\displaystyle\frac{2^{\ell}\ell!}{(2\ell+1)!}=\frac{1}{(2\ell+1% )!!}}}
\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}		 ℜ ⁡ ( ℓ + 1 + i ⁢ η ) > 0 ℓ 1 imaginary-unit 𝜂 0 {\displaystyle{\displaystyle\Re(\ell+1+\mathrm{i}\eta)>0}} 
((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))

Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]
Failure Failure Error
Failed [1 / 1]
Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]]
Test Values: {}

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