28.25: 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/28.25.E3 28.25.E3] || [[Item:Q8414|<math>(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(+)+((m +(1)/(2))^(2)+(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(+)+(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(+) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(+)+((m +Divide[1,2])^(2)+(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(+)+(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(+) == 0</syntaxhighlight> || Error || Failure || - || Error
| [https://dlmf.nist.gov/28.25.E3 28.25.E3] || <math qid="Q8414">(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(+)+((m +(1)/(2))^(2)+(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(+)+(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(+) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(+)+((m +Divide[1,2])^(2)+(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(+)+(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(+) == 0</syntaxhighlight> || Error || Failure || - || Error
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| [https://dlmf.nist.gov/28.25.E3 28.25.E3] || [[Item:Q8414|<math>(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(-)+((m +(1)/(2))^(2)-(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(-)-(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(-) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(-)+((m +Divide[1,2])^(2)-(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(-)-(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(-) == 0</syntaxhighlight> || Error || Failure || - || Error
| [https://dlmf.nist.gov/28.25.E3 28.25.E3] || <math qid="Q8414">(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(-)+((m +(1)/(2))^(2)-(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(-)-(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(-) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(-)+((m +Divide[1,2])^(2)-(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(-)-(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(-) == 0</syntaxhighlight> || Error || Failure || - || Error
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Latest revision as of 12:08, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
28.25.E3 ( m + 1 ) ⁢ D m + 1 + + ( ( m + 1 2 ) 2 + ( m + 1 4 ) ⁢ 8 ⁢ i ⁢ h + 2 ⁢ h 2 - a ) ⁢ D m + + ( m - 1 2 ) ⁢ ( 8 ⁢ i ⁢ h ⁢ m ) ⁢ D m - 1 + = 0 𝑚 1 subscript superscript 𝐷 𝑚 1 superscript 𝑚 1 2 2 𝑚 1 4 8 imaginary-unit ℎ 2 superscript ℎ 2 𝑎 subscript superscript 𝐷 𝑚 𝑚 1 2 8 imaginary-unit ℎ 𝑚 superscript subscript 𝐷 𝑚 1 0 {\displaystyle{\displaystyle(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+% \tfrac{1}{4})8\mathrm{i}h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8% \mathrm{i}hm\right)D_{m-1}^{+}=0}}
(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0		 m ≥ 0 𝑚 0 {\displaystyle{\displaystyle m\geq 0}} 
(m + 1)*(D[m + 1])^(+)+((m +(1)/(2))^(2)+(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(+)+(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(+) = 0

(m + 1)*(Subscript[D, m + 1])^(+)+((m +Divide[1,2])^(2)+(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(+)+(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(+) == 0
Error Failure - Error
28.25.E3 ( m + 1 ) ⁢ D m + 1 - + ( ( m + 1 2 ) 2 - ( m + 1 4 ) ⁢ 8 ⁢ i ⁢ h + 2 ⁢ h 2 - a ) ⁢ D m - - ( m - 1 2 ) ⁢ ( 8 ⁢ i ⁢ h ⁢ m ) ⁢ D m - 1 - = 0 𝑚 1 subscript superscript 𝐷 𝑚 1 superscript 𝑚 1 2 2 𝑚 1 4 8 imaginary-unit ℎ 2 superscript ℎ 2 𝑎 subscript superscript 𝐷 𝑚 𝑚 1 2 8 imaginary-unit ℎ 𝑚 superscript subscript 𝐷 𝑚 1 0 {\displaystyle{\displaystyle(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+% \tfrac{1}{4})8\mathrm{i}h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8% \mathrm{i}hm\right)D_{m-1}^{-}=0}}
(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0		 m ≥ 0 𝑚 0 {\displaystyle{\displaystyle m\geq 0}} 
(m + 1)*(D[m + 1])^(-)+((m +(1)/(2))^(2)-(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(-)-(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(-) = 0

(m + 1)*(Subscript[D, m + 1])^(-)+((m +Divide[1,2])^(2)-(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(-)-(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(-) == 0
Error Failure - Error
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