9.13: 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
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex7 9.13#Ex7] || [[Item:Q2976|<math>m = n+2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m = n+2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m = n + 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m == n + 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/9.13#Ex7 9.13#Ex7] || <math qid="Q2976">m = n+2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m = n+2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m = n + 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m == n + 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex8 9.13#Ex8] || [[Item:Q2977|<math>t = (\tfrac{1}{2}m)^{-2/m}z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t = (\tfrac{1}{2}m)^{-2/m}z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t = ((1)/(2)*m)^(- 2/m)* z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t == (Divide[1,2]*m)^(- 2/m)* z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/9.13#Ex8 9.13#Ex8] || <math qid="Q2977">t = (\tfrac{1}{2}m)^{-2/m}z</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t = (\tfrac{1}{2}m)^{-2/m}z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t = ((1)/(2)*m)^(- 2/m)* z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t == (Divide[1,2]*m)^(- 2/m)* z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
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| [https://dlmf.nist.gov/9.13.E20 9.13.E20] || [[Item:Q2983|<math>U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>U[1](x , alpha) = (1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 1][x , \[Alpha]] == Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]</syntaxhighlight> || Failure || Failure || Error || Error
| [https://dlmf.nist.gov/9.13.E20 9.13.E20] || <math qid="Q2983">U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>U[1](x , alpha) = (1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 1][x , \[Alpha]] == Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]</syntaxhighlight> || Failure || Failure || Error || Error
|-  
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| [https://dlmf.nist.gov/9.13.E21 9.13.E21] || [[Item:Q2984|<math>U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = (alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == (\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]</syntaxhighlight> || Failure || Failure || Error || Error
| [https://dlmf.nist.gov/9.13.E21 9.13.E21] || <math qid="Q2984">U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = (alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == (\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]</syntaxhighlight> || Failure || Failure || Error || Error
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex9 9.13#Ex9] || [[Item:Q2985|<math>\alpha = m-2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = m-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = m - 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == m - 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/9.13#Ex9 9.13#Ex9] || <math qid="Q2985">\alpha = m-2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = m-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = m - 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == m - 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/9.13#Ex10 9.13#Ex10] || [[Item:Q2986|<math>x = (m/2)^{2/m}t</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = (m/2)^{2/m}t</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = (m/2)^(2/m)* t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == (m/2)^(2/m)* t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/9.13#Ex10 9.13#Ex10] || <math qid="Q2986">x = (m/2)^{2/m}t</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = (m/2)^{2/m}t</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = (m/2)^(2/m)* t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == (m/2)^(2/m)* t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
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| [https://dlmf.nist.gov/9.13.E23 9.13.E23] || [[Item:Q2987|<math>U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</syntaxhighlight> || <math>\realpart@@{(1/m)} > 0</math> || <syntaxhighlight lang=mathematica>U[1](x , alpha) = ((Pi)^(1/2))/((2)^((m + 2)/(2*m))* GAMMA(1/m))*(W[m](t)+ W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 1][x , \[Alpha]] == Divide[(Pi)^(1/2),(2)^((m + 2)/(2*m))* Gamma[1/m]]*(Subscript[W, m][t]+ Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
| [https://dlmf.nist.gov/9.13.E23 9.13.E23] || <math qid="Q2987">U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)</syntaxhighlight> || <math>\realpart@@{(1/m)} > 0</math> || <syntaxhighlight lang=mathematica>U[1](x , alpha) = ((Pi)^(1/2))/((2)^((m + 2)/(2*m))* GAMMA(1/m))*(W[m](t)+ W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 1][x , \[Alpha]] == Divide[(Pi)^(1/2),(2)^((m + 2)/(2*m))* Gamma[1/m]]*(Subscript[W, m][t]+ Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
|-  
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| [https://dlmf.nist.gov/9.13.E24 9.13.E24] || [[Item:Q2988|<math>U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)</syntaxhighlight> || <math>\realpart@@{(-1/m)} > 0</math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = ((Pi)^(1/2)* (m)^(2/m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/m))*(W[m](t)- W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == Divide[(Pi)^(1/2)* (m)^(2/m),(2)^((m + 2)/(2*m))* Gamma[- 1/m]]*(Subscript[W, m][t]- Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
| [https://dlmf.nist.gov/9.13.E24 9.13.E24] || <math qid="Q2988">U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)</syntaxhighlight> || <math>\realpart@@{(-1/m)} > 0</math> || <syntaxhighlight lang=mathematica>U[2](x , alpha) = ((Pi)^(1/2)* (m)^(2/m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/m))*(W[m](t)- W[m](- t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[U, 2][x , \[Alpha]] == Divide[(Pi)^(1/2)* (m)^(2/m),(2)^((m + 2)/(2*m))* Gamma[- 1/m]]*(Subscript[W, m][t]- Subscript[W, m][- t])</syntaxhighlight> || Failure || Failure || Error || Error
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Latest revision as of 11:21, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
9.13#Ex7 m = n + 2 𝑚 𝑛 2 {\displaystyle{\displaystyle m=n+2}}
m = n+2		 

m = n + 2
 
m == n + 2
 Skipped - no semantic math Skipped - no semantic math - -
9.13#Ex8 t = ( 1 2 ⁢ m ) - 2 / m ⁢ z 𝑡 superscript 1 2 𝑚 2 𝑚 𝑧 {\displaystyle{\displaystyle t=(\tfrac{1}{2}m)^{-2/m}z}}
t = (\tfrac{1}{2}m)^{-2/m}z		 

t = ((1)/(2)*m)^(- 2/m)* z
 
t == (Divide[1,2]*m)^(- 2/m)* z
 Skipped - no semantic math Skipped - no semantic math - -
9.13.E20 U 1 ⁢ ( x , α ) = 1 ( α + 2 ) 1 / ( α + 2 ) ⁢ Γ ⁡ ( α + 1 α + 2 ) ⁢ x 1 / 2 ⁢ J - 1 / ( α + 2 ) ⁡ ( 2 α + 2 ⁢ x ( α + 2 ) / 2 ) subscript 𝑈 1 𝑥 𝛼 1 superscript 𝛼 2 1 𝛼 2 Euler-Gamma 𝛼 1 𝛼 2 superscript 𝑥 1 2 Bessel-J 1 𝛼 2 2 𝛼 2 superscript 𝑥 𝛼 2 2 {\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{1}{(\alpha+2)^{1/(\alpha+2)% }}\*\Gamma\left(\frac{\alpha+1}{\alpha+2}\right)x^{1/2}J_{-1/(\alpha+2)}\left(% \frac{2}{\alpha+2}x^{(\alpha+2)/2}\right)}}
U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}		 

U[1](x , alpha) = (1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))

Subscript[U, 1][x , \[Alpha]] == Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]
Failure Failure Error Error
9.13.E21 U 2 ⁢ ( x , α ) = ( α + 2 ) 1 / ( α + 2 ) ⁢ Γ ⁡ ( α + 3 α + 2 ) ⁢ x 1 / 2 ⁢ J 1 / ( α + 2 ) ⁡ ( 2 α + 2 ⁢ x ( α + 2 ) / 2 ) subscript 𝑈 2 𝑥 𝛼 superscript 𝛼 2 1 𝛼 2 Euler-Gamma 𝛼 3 𝛼 2 superscript 𝑥 1 2 Bessel-J 1 𝛼 2 2 𝛼 2 superscript 𝑥 𝛼 2 2 {\displaystyle{\displaystyle U_{2}(x,\alpha)=(\alpha+2)^{1/(\alpha+2)}\*\Gamma% \left(\frac{\alpha+3}{\alpha+2}\right)x^{1/2}J_{1/(\alpha+2)}\left(\frac{2}{% \alpha+2}x^{(\alpha+2)/2}\right)}}
U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}		 

U[2](x , alpha) = (alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))

Subscript[U, 2][x , \[Alpha]] == (\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]
Failure Failure Error Error
9.13#Ex9 α = m - 2 𝛼 𝑚 2 {\displaystyle{\displaystyle\alpha=m-2}}
\alpha = m-2		 

alpha = m - 2
 
\[Alpha] == m - 2
 Skipped - no semantic math Skipped - no semantic math - -
9.13#Ex10 x = ( m / 2 ) 2 / m ⁢ t 𝑥 superscript 𝑚 2 2 𝑚 𝑡 {\displaystyle{\displaystyle x=(m/2)^{2/m}t}}
x = (m/2)^{2/m}t		 

x = (m/2)^(2/m)* t
 
x == (m/2)^(2/m)* t
 Skipped - no semantic math Skipped - no semantic math - -
9.13.E23 U 1 ⁢ ( x , α ) = π 1 / 2 2 ( m + 2 ) / ( 2 ⁢ m ) ⁢ Γ ⁡ ( 1 / m ) ⁢ ( W m ⁢ ( t ) + W m ⁢ ( - t ) ) subscript 𝑈 1 𝑥 𝛼 superscript 𝜋 1 2 superscript 2 𝑚 2 2 𝑚 Euler-Gamma 1 𝑚 subscript 𝑊 𝑚 𝑡 subscript 𝑊 𝑚 𝑡 {\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{\pi^{1/2}}{2^{(m+2)/(2m)}% \Gamma\left(1/m\right)}\left(W_{m}(t)+W_{m}(-t)\right)}}
U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)		 ℜ ⁡ ( 1 / m ) > 0 1 𝑚 0 {\displaystyle{\displaystyle\Re(1/m)>0}} 
U[1](x , alpha) = ((Pi)^(1/2))/((2)^((m + 2)/(2*m))* GAMMA(1/m))*(W[m](t)+ W[m](- t))

Subscript[U, 1][x , \[Alpha]] == Divide[(Pi)^(1/2),(2)^((m + 2)/(2*m))* Gamma[1/m]]*(Subscript[W, m][t]+ Subscript[W, m][- t])
Failure Failure Error Error
9.13.E24 U 2 ⁢ ( x , α ) = π 1 / 2 ⁢ m 2 / m 2 ( m + 2 ) / ( 2 ⁢ m ) ⁢ Γ ⁡ ( - 1 / m ) ⁢ ( W m ⁢ ( t ) - W m ⁢ ( - t ) ) subscript 𝑈 2 𝑥 𝛼 superscript 𝜋 1 2 superscript 𝑚 2 𝑚 superscript 2 𝑚 2 2 𝑚 Euler-Gamma 1 𝑚 subscript 𝑊 𝑚 𝑡 subscript 𝑊 𝑚 𝑡 {\displaystyle{\displaystyle U_{2}(x,\alpha)=\frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/% (2m)}\Gamma\left(-1/m\right)}\left(W_{m}(t){-}W_{m}(-t)\right)}}
U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)		 ℜ ⁡ ( - 1 / m ) > 0 1 𝑚 0 {\displaystyle{\displaystyle\Re(-1/m)>0}} 
U[2](x , alpha) = ((Pi)^(1/2)* (m)^(2/m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/m))*(W[m](t)- W[m](- t))

Subscript[U, 2][x , \[Alpha]] == Divide[(Pi)^(1/2)* (m)^(2/m),(2)^((m + 2)/(2*m))* Gamma[- 1/m]]*(Subscript[W, m][t]- Subscript[W, m][- t])
Failure Failure Error Error
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