Coulomb Functions - 33.6 Power-Series Expansions in
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k+\ell)(k-\ell-1)A_{k}^{\ell} = 2\eta A_{k-1}^{\ell}-A_{k-2}^{\ell}}
(k+\ell)(k-\ell-1)A_{k}^{\ell} = 2\eta A_{k-1}^{\ell}-A_{k-2}^{\ell} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \ell+3} | (k + ell)*(k - ell - 1)*(A[k])^(ell) = 2*eta*(A[k - 1])^(ell)- (A[k - 2])^(ell) |
(k + \[ScriptL])*(k - \[ScriptL]- 1)*(Subscript[A, k])^\[ScriptL] == 2*\[Eta]*(Subscript[A, k - 1])^\[ScriptL]- (Subscript[A, k - 2])^\[ScriptL] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k}^{\ell}(\eta) = \dfrac{(-\iunit)^{k-\ell-1}}{(k-\ell-1)!}\*\genhyperF{2}{1}@{\ell+1-k,\ell+1-\iunit\eta}{2\ell+2}{2}}
A_{k}^{\ell}(\eta) = \dfrac{(-\iunit)^{k-\ell-1}}{(k-\ell-1)!}\*\genhyperF{2}{1}@{\ell+1-k,\ell+1-\iunit\eta}{2\ell+2}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (A[k])^(ell)(eta) = ((- I)^(k - ell - 1))/(factorial(k - ell - 1))* hypergeom([ell + 1 - k , ell + 1 - I*eta], [2*ell + 2], 2)
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(Subscript[A, k])^\[ScriptL][\[Eta]] == Divide[(- I)^(k - \[ScriptL]- 1),(k - \[ScriptL]- 1)!]* HypergeometricPFQ[{\[ScriptL]+ 1 - k , \[ScriptL]+ 1 - I*\[Eta]}, {2*\[ScriptL]+ 2}, 2]
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Failure | Failure | Error | Failed [293 / 300]
Result: Complex[0.5000000000000001, 0.8660254037844386]
Test Values: {Rule[k, 1], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.0, 1.0]
Test Values: {Rule[k, 1], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |