Orthogonal Polynomials - 18.39 Physical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.39.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(x) = \tfrac{1}{2}m\omega^{2}x^{2}}
V(x) = \tfrac{1}{2}m\omega^{2}x^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | V(x) = (1)/(2)*m*(omega)^(2)* (x)^(2) |
V[x] == Divide[1,2]*m*\[Omega]^(2)* (x)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 18.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}}}
\eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | eta[n](x) = (Pi)^(-(1)/(4))* (2)^(-(1)/(2)*n)*(factorial(n)*b)^(-(1)/(2))* HermiteH(n, x/b)*exp(- (x)^(2)/2*(b)^(2))
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Subscript[\[Eta], n][x] == (Pi)^(-Divide[1,4])* (2)^(-Divide[1,2]*n)*((n)!*b)^(-Divide[1,2])* HermiteH[n, x/b]*Exp[- (x)^(2)/2*(b)^(2)]
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Failure | Failure | Failed [300 / 300] Result: 1.299038106+.6809960435*I
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: 1.299038106+.7845019783*I
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[1.299038105676658, 0.6809960434853285]
Test Values: {Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[1.299038105676658, 0.7845019782573356]
Test Values: {Rule[b, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |