Orthogonal Polynomials - 18.38 Mathematical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.38.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{n}(x) = \ifrac{2n\HermitepolyH{n+1}@{x}\HermitepolyH{n-1}@{x}}{(\HermitepolyH{n}@{x})^{2}}}
V_{n}(x) = \ifrac{2n\HermitepolyH{n+1}@{x}\HermitepolyH{n-1}@{x}}{(\HermitepolyH{n}@{x})^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | V[n](x) = (2*n*HermiteH(n + 1, x)*HermiteH(n - 1, x))/((HermiteH(n, x))^(2))
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Subscript[V, n][x] == Divide[2*n*HermiteH[n + 1, x]*HermiteH[n - 1, x],(HermiteH[n, x])^(2)]
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Failure | Aborted | Failed [90 / 90] Result: -.256517449+.7500000000*I
Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: -.905043527+.7500000000*I
Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Failed [90 / 90]
Result: Complex[-0.25651744987889735, 0.7499999999999999]
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-0.905043526976403, 0.7499999999999999]
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 18.38.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{m=0}^{n}\JacobipolyP{\alpha}{0}{m}@{x} \geq 0}
\sum_{m=0}^{n}\JacobipolyP{\alpha}{0}{m}@{x} \geq 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 \leq x, x \leq 1, \alpha > -1} | sum(JacobiP(m, alpha, 0, x), m = 0..n) >= 0
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Sum[JacobiP[m, \[Alpha], 0, x], {m, 0, n}, GenerateConditions->None] >= 0
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 27] |