Asymptotic Approximations - 2.9 Difference Equations
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 2.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho^{2}+f_{0}\rho+g_{0} = 0}
\rho^{2}+f_{0}\rho+g_{0} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (rho)^(2)+ f[0]*rho + g[0] = 0 |
\[Rho]^(2)+ Subscript[f, 0]*\[Rho]+ Subscript[g, 0] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 2.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{j} = (f_{1}\rho_{j}+g_{1})/(f_{0}\rho_{j}+2g_{0})}
\alpha_{j} = (f_{1}\rho_{j}+g_{1})/(f_{0}\rho_{j}+2g_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha[j] = (f[1]*rho[j]+ g[1])/(f[0]*rho[j]+ 2*g[0]) |
Subscript[\[Alpha], j] == (Subscript[f, 1]*Subscript[\[Rho], j]+ Subscript[g, 1])/(Subscript[f, 0]*Subscript[\[Rho], j]+ 2*Subscript[g, 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 2.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{j}(f_{0}+2\rho_{j})sa_{s,j} = \sum_{r=1}^{s}\left(\rho_{j}^{2}2^{r+1}\binom{\alpha_{j}+r-s}{r+1}+\rho_{j}\sum_{q=0}^{r+1}\binom{\alpha_{j}+r-s}{r+1-q}f_{q}+g_{r+1}\right)a_{s-r,j}}
\rho_{j}(f_{0}+2\rho_{j})sa_{s,j} = \sum_{r=1}^{s}\left(\rho_{j}^{2}2^{r+1}\binom{\alpha_{j}+r-s}{r+1}+\rho_{j}\sum_{q=0}^{r+1}\binom{\alpha_{j}+r-s}{r+1-q}f_{q}+g_{r+1}\right)a_{s-r,j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | rho[j]*(f[0]+ 2*rho[j])*s*a[s , j] = sum(((rho[j])^(2)*(2)^(r + 1)*binomial(alpha[j]+ r - s,r + 1)+ rho[j]*sum(binomial(alpha[j]+ r - s,r + 1 - q)*f[q], q = 0..r + 1)+ g[r + 1])*a[s - r , j], r = 1..s)
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Subscript[\[Rho], j]*(Subscript[f, 0]+ 2*Subscript[\[Rho], j])*s*Subscript[a, s , j] == Sum[((Subscript[\[Rho], j])^(2)*(2)^(r + 1)*Binomial[Subscript[\[Alpha], j]+ r - s,r + 1]+ Subscript[\[Rho], j]*Sum[Binomial[Subscript[\[Alpha], j]+ r - s,r + 1 - q]*Subscript[f, q], {q, 0, r + 1}, GenerateConditions->None]+ Subscript[g, r + 1])*Subscript[a, s - r , j], {r, 1, s}, GenerateConditions->None]
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Failure | Failure | Error | Failed [1 / 1]
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| 2.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{g_{0}}\kappa = \sqrt{2f_{0}f_{1}-4g_{1}}}
\sqrt{g_{0}}\kappa = \sqrt{2f_{0}f_{1}-4g_{1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4g_{0}\alpha = g_{0}+2g_{1}} | sqrt(g[0])*kappa = sqrt(2*f[0]*f[1]- 4*g[1]) |
Sqrt[Subscript[g, 0]]*\[Kappa] == Sqrt[2*Subscript[f, 0]*Subscript[f, 1]- 4*Subscript[g, 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 2.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2g_{0}\alpha^{2}-(f_{0}f_{1}+2g_{0})\alpha+2g_{2}-f_{0}f_{2} = 0}
2g_{0}\alpha^{2}-(f_{0}f_{1}+2g_{0})\alpha+2g_{2}-f_{0}f_{2} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 2*g[0]*(alpha)^(2)-(f[0]*f[1]+ 2*g[0])*alpha + 2*g[2]- f[0]*f[2] = 0 |
2*Subscript[g, 0]*\[Alpha]^(2)-(Subscript[f, 0]*Subscript[f, 1]+ 2*Subscript[g, 0])*\[Alpha]+ 2*Subscript[g, 2]- Subscript[f, 0]*Subscript[f, 2] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |