Heun Functions - 31.17 Physical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x_{s}^{2}}{z_{k}}+\frac{x_{t}^{2}}{z_{k}-1}+\frac{x_{u}^{2}}{z_{k}-a} = 0}
\frac{x_{s}^{2}}{z_{k}}+\frac{x_{t}^{2}}{z_{k}-1}+\frac{x_{u}^{2}}{z_{k}-a} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | ((x[s])^(2))/(x + y*I[k])+((x[t])^(2))/(x + y*I[k]- 1)+((x[u])^(2))/(x + y*I[k]- a) = 0 |
Divide[(Subscript[x, s])^(2),Subscript[x + y*I, k]]+Divide[(Subscript[x, t])^(2),Subscript[x + y*I, k]- 1]+Divide[(Subscript[x, u])^(2),Subscript[x + y*I, k]- a] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Psi(\mathbf{x}) = (z_{1}z_{2})^{-s-\frac{1}{4}}((z_{1}-1)(z_{2}-1))^{-t-\frac{1}{4}}\*((z_{1}-a)(z_{2}-a))^{-u-\frac{1}{4}}w(z_{1})w(z_{2})}
\Psi(\mathbf{x}) = (z_{1}z_{2})^{-s-\frac{1}{4}}((z_{1}-1)(z_{2}-1))^{-t-\frac{1}{4}}\*((z_{1}-a)(z_{2}-a))^{-u-\frac{1}{4}}w(z_{1})w(z_{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Psi(x) = (x + y*I[1]*x + y*I[2])^(- s -(1)/(4))*((x + y*I[1]- 1)*(x + y*I[2]- 1))^(- t -(1)/(4))*((x + y*I[1]- a)*(x + y*I[2]- a))^(- u -(1)/(4))* w*(x + y*I[1])*w*(x + y*I[2]) |
\[CapitalPsi][x] == (Subscript[x + y*I, 1]*Subscript[x + y*I, 2])^(- s -Divide[1,4])*((Subscript[x + y*I, 1]- 1)*(Subscript[x + y*I, 2]- 1))^(- t -Divide[1,4])*((Subscript[x + y*I, 1]- a)*(Subscript[x + y*I, 2]- a))^(- u -Divide[1,4])* w*(Subscript[x + y*I, 1])*w*(Subscript[x + y*I, 2]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = -s-t-u-j-1}
\alpha = -s-t-u-j-1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha = - s - t - u - j - 1 |
\[Alpha] == - s - t - u - j - 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = j-s-t-u}
\beta = j-s-t-u |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta = j - s - t - u |
\[Beta] == j - s - t - u |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = -2s}
\gamma = -2s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | gamma = - 2*s |
\[Gamma] == - 2*s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = -2t}
\delta = -2t |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | delta = - 2*t |
\[Delta] == - 2*t |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = -2u}
\epsilon = -2u |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | epsilon = - 2*u |
\[Epsilon] == - 2*u |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.17#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = ah_{s}+2s(at+u)}
q = ah_{s}+2s(at+u) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q = a*h[s]+ 2*s*(a*t + u) |
q == a*Subscript[h, s]+ 2*s*(a*t + u) |
Skipped - no semantic math | Skipped - no semantic math | - | - |