10.13: 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/10.13.E8 10.13.E8] || [[Item:Q3133|<math>w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w</syntaxhighlight> || <math>w = z^{\frac{1}{2}n}\BesselC{n}@{2\lambda e^{k\pi\iunit/n}z^{\frac{1}{2}}}, k = 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(w)^(2*n) = (- 1)^(n)* (lambda)^(2*n)* (z)^(- n)* w</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(w)^(2*n) == (- 1)^(n)* \[Lambda]^(2*n)* (z)^(- n)* w</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/10.13.E8 10.13.E8] || <math qid="Q3133">w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w</syntaxhighlight> || <math>w = z^{\frac{1}{2}n}\BesselC{n}@{2\lambda e^{k\pi\iunit/n}z^{\frac{1}{2}}}, k = 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(w)^(2*n) = (- 1)^(n)* (lambda)^(2*n)* (z)^(- n)* w</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(w)^(2*n) == (- 1)^(n)* \[Lambda]^(2*n)* (z)^(- n)* w</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/10.13.E11 10.13.E11] || [[Item:Q3136|<math>\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0</syntaxhighlight> || <math>w = \BesselC{\nu}@{z}\mathscr{D}_{\mu}(z).</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((vartheta)^(4)- 2*((nu)^(2)+ (mu)^(2))*(vartheta)^(2)+((nu)^(2)- (mu)^(2))^(2))*w + 4*(z)^(2)*(vartheta + 1)*(vartheta + 2)*w = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[CurlyTheta]^(4)- 2*(\[Nu]^(2)+ \[Mu]^(2))*\[CurlyTheta]^(2)+(\[Nu]^(2)- \[Mu]^(2))^(2))*w + 4*(z)^(2)*(\[CurlyTheta]+ 1)*(\[CurlyTheta]+ 2)*w == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/10.13.E11 10.13.E11] || <math qid="Q3136">\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0</syntaxhighlight> || <math>w = \BesselC{\nu}@{z}\mathscr{D}_{\mu}(z).</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((vartheta)^(4)- 2*((nu)^(2)+ (mu)^(2))*(vartheta)^(2)+((nu)^(2)- (mu)^(2))^(2))*w + 4*(z)^(2)*(vartheta + 1)*(vartheta + 2)*w = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[CurlyTheta]^(4)- 2*(\[Nu]^(2)+ \[Mu]^(2))*\[CurlyTheta]^(2)+(\[Nu]^(2)- \[Mu]^(2))^(2))*w + 4*(z)^(2)*(\[CurlyTheta]+ 1)*(\[CurlyTheta]+ 2)*w == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 11:23, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.13.E8 w ( 2 ⁢ n ) = ( - 1 ) n ⁢ λ 2 ⁢ n ⁢ z - n ⁢ w superscript 𝑤 2 𝑛 superscript 1 𝑛 superscript 𝜆 2 𝑛 superscript 𝑧 𝑛 𝑤 {\displaystyle{\displaystyle w^{(2n)}=(-1)^{n}\lambda^{2n}z^{-n}w}}
w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w		 w = z 1 2 ⁢ n ⁢ 𝒞 n ⁡ ( 2 ⁢ λ ⁢ e k ⁢ π ⁢ i / n ⁢ z 1 2 ) , k = 0 formulae-sequence 𝑤 superscript 𝑧 1 2 𝑛 cylinder-function 𝑛 2 𝜆 superscript 𝑒 𝑘 𝜋 imaginary-unit 𝑛 superscript 𝑧 1 2 𝑘 0 {\displaystyle{\displaystyle w=z^{\frac{1}{2}n}\mathscr{C}_{n}\left(2\lambda e% ^{k\pi\mathrm{i}/n}z^{\frac{1}{2}}\right),k=0}} 
(w)^(2*n) = (- 1)^(n)* (lambda)^(2*n)* (z)^(- n)* w
 
(w)^(2*n) == (- 1)^(n)* \[Lambda]^(2*n)* (z)^(- n)* w
 Skipped - no semantic math Skipped - no semantic math - -
10.13.E11 ( ϑ 4 - 2 ⁢ ( ν 2 + μ 2 ) ⁢ ϑ 2 + ( ν 2 - μ 2 ) 2 ) ⁢ w + 4 ⁢ z 2 ⁢ ( ϑ + 1 ) ⁢ ( ϑ + 2 ) ⁢ w = 0 superscript italic-ϑ 4 2 superscript 𝜈 2 superscript 𝜇 2 superscript italic-ϑ 2 superscript superscript 𝜈 2 superscript 𝜇 2 2 𝑤 4 superscript 𝑧 2 italic-ϑ 1 italic-ϑ 2 𝑤 0 {\displaystyle{\displaystyle\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2% }+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w=0}}
\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0		 w = 𝒞 ν ⁡ ( z ) ⁢ 𝒟 μ ⁢ ( z ) . 𝑤 cylinder-function 𝜈 𝑧 subscript 𝒟 𝜇 𝑧 {\displaystyle{\displaystyle w=\mathscr{C}_{\nu}\left(z\right)\mathscr{D}_{\mu% }(z).}} 
((vartheta)^(4)- 2*((nu)^(2)+ (mu)^(2))*(vartheta)^(2)+((nu)^(2)- (mu)^(2))^(2))*w + 4*(z)^(2)*(vartheta + 1)*(vartheta + 2)*w = 0
 
(\[CurlyTheta]^(4)- 2*(\[Nu]^(2)+ \[Mu]^(2))*\[CurlyTheta]^(2)+(\[Nu]^(2)- \[Mu]^(2))^(2))*w + 4*(z)^(2)*(\[CurlyTheta]+ 1)*(\[CurlyTheta]+ 2)*w == 0
 Skipped - no semantic math Skipped - no semantic math - -
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