Coulomb Functions - 33.14 Definitions and Basic Properties
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{r}+\left(\epsilon+\frac{2}{r}-\frac{\ell(\ell+1)}{r^{2}}\right)w = 0}
\deriv[2]{w}{r}+\left(\epsilon+\frac{2}{r}-\frac{\ell(\ell+1)}{r^{2}}\right)w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(w, [r$(2)])+(epsilon +(2)/(r)-(ell*(ell + 1))/((r)^(2)))*w = 0
|
D[w, {r, 2}]+(\[Epsilon]+Divide[2,r]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(r)^(2)])*w == 0
|
Failure | Failure | Error | Failed [300 / 300]
Result: Complex[-1.0584754935143141, -0.611111111111111]
Test Values: {Rule[r, Rational[-3, 2]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[ϵ, 1]}
Result: Complex[-0.19245008972987526, -0.11111111111111109]
Test Values: {Rule[r, Rational[-3, 2]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[ϵ, 2]}
... skip entries to safe data |
| 33.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = -\eta\rho}
r = -\eta\rho |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | r = - eta*rho |
r == - \[Eta]*\[Rho] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = 1/\eta^{2}}
\epsilon = 1/\eta^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | epsilon = 1/(eta)^(2) |
\[Epsilon] == 1/\[Eta]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.14.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A(\epsilon,\ell) = \frac{\EulerGamma@{1+\ell+\kappa}}{\EulerGamma@{\kappa-\ell}}\kappa^{-2\ell-1}}
A(\epsilon,\ell) = \frac{\EulerGamma@{1+\ell+\kappa}}{\EulerGamma@{\kappa-\ell}}\kappa^{-2\ell-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1+\ell+\kappa)} > 0, \realpart@@{(\kappa-\ell)} > 0} | (product(1 + epsilon*(k)^(2), k = 0..ell)) = (GAMMA(1 + ell + kappa))/(GAMMA(kappa - ell))*(kappa)^(- 2*ell - 1)
|
(Product[1 + \[Epsilon]*(k)^(2), {k, 0, \[ScriptL]}, GenerateConditions->None]) == Divide[Gamma[1 + \[ScriptL]+ \[Kappa]],Gamma[\[Kappa]- \[ScriptL]]]*\[Kappa]^(- 2*\[ScriptL]- 1)
|
Failure | Failure | Error | Failed [6 / 6]
Result: 1.4444444444444444
Test Values: {Rule[ℓ, 1], Rule[ϵ, 1], Rule[κ, Rational[3, 2]]}
Result: Complex[2.4444444444444446, 0.0]
Test Values: {Rule[ℓ, 1], Rule[ϵ, 2], Rule[κ, Rational[3, 2]]}
... skip entries to safe data |