Mathieu Functions and Hill’s Equation - 28.25 Asymptotic Expansions for Large
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.25.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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+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 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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+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 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 |