Coulomb Functions - 33.20 Expansions for Small
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\sf F}_{k}(\ell;r) = \sum_{p=2k}^{3k}(2r)^{(p+1)/2}C_{k,p}\BesselJ{2\ell+1+p}@{\sqrt{8r}}}
{\sf F}_{k}(\ell;r) = \sum_{p=2k}^{3k}(2r)^{(p+1)/2}C_{k,p}\BesselJ{2\ell+1+p}@{\sqrt{8r}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r > 0, \realpart@@{((2\ell+1+p)+k+1)} > 0} | F[k](ell ; r) = sum((2*r)^((p + 1)/2)* C[k , p]*BesselJ(2*ell + 1 + p, sqrt(8*r)), p = 2*k..3*k)
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Subscript[F, k][\[ScriptL]; r] == Sum[(2*r)^((p + 1)/2)* Subscript[C, k , p]*BesselJ[2*\[ScriptL]+ 1 + p, Sqrt[8*r]], {p, 2*k, 3*k}, GenerateConditions->None]
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Translation Error | Translation Error | - | - |
| 33.20.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\sf F}_{k}(\ell;r) = \sum_{p=2k}^{3k}(-1)^{\ell+1+p}(2|r|)^{(p+1)/2}C_{k,p}\modBesselI{2\ell+1+p}@{\sqrt{8|r|}}}
{\sf F}_{k}(\ell;r) = \sum_{p=2k}^{3k}(-1)^{\ell+1+p}(2|r|)^{(p+1)/2}C_{k,p}\modBesselI{2\ell+1+p}@{\sqrt{8|r|}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r < 0, \realpart@@{((2\ell+1+p)+k+1)} > 0} | F[k](ell ; r) = sum((- 1)^(ell + 1 + p)*(2*abs(r))^((p + 1)/2)* C[k , p]*BesselI(2*ell + 1 + p, sqrt(8*abs(r))), p = 2*k..3*k)
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Subscript[F, k][\[ScriptL]; r] == Sum[(- 1)^(\[ScriptL]+ 1 + p)*(2*Abs[r])^((p + 1)/2)* Subscript[C, k , p]*BesselI[2*\[ScriptL]+ 1 + p, Sqrt[8*Abs[r]]], {p, 2*k, 3*k}, GenerateConditions->None]
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Translation Error | Translation Error | - | - |
| 33.20#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{k,p} = 0}
C_{k,p} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p < 2k, p > 3k} | C[k , p] = 0 |
Subscript[C, k , p] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.20#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{k,p} = \left(-(2\ell+p)C_{k-1,p-2}+C_{k-1,p-3}\right)/(4p)}
C_{k,p} = \left(-(2\ell+p)C_{k-1,p-2}+C_{k-1,p-3}\right)/(4p) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k > 0, 2k \leq p, p \leq 3k} | C[k , p] = (-(2*ell + p)*C[k - 1 , p - 2]+ C[k - 1 , p - 3])/(4*p) |
Subscript[C, k , p] == (-(2*\[ScriptL]+ p)*Subscript[C, k - 1 , p - 2]+ Subscript[C, k - 1 , p - 3])/(4*p) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.20.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\sf H}_{k}(\ell;r) = \sum_{p=2k}^{3k}(2r)^{(p+1)/2}C_{k,p}\BesselY{2\ell+1+p}@{\sqrt{8r}}}
{\sf H}_{k}(\ell;r) = \sum_{p=2k}^{3k}(2r)^{(p+1)/2}C_{k,p}\BesselY{2\ell+1+p}@{\sqrt{8r}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r > 0, \realpart@@{((2\ell+1+p)+k+1)} > 0, \realpart@@{((-(2\ell+1+p))+k+1)} > 0} | H[k](ell ; r) = sum((2*r)^((p + 1)/2)* C[k , p]*BesselY(2*ell + 1 + p, sqrt(8*r)), p = 2*k..3*k)
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Subscript[H, k][\[ScriptL]; r] == Sum[(2*r)^((p + 1)/2)* Subscript[C, k , p]*BesselY[2*\[ScriptL]+ 1 + p, Sqrt[8*r]], {p, 2*k, 3*k}, GenerateConditions->None]
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Translation Error | Translation Error | - | - |
| 33.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\sf H}_{k}(\ell;r) = (-1)^{\ell+1}\frac{2}{\pi}\sum_{p=2k}^{3k}(2|r|)^{(p+1)/2}C_{k,p}\modBesselK{2\ell+1+p}@{\sqrt{8|r|}}}
{\sf H}_{k}(\ell;r) = (-1)^{\ell+1}\frac{2}{\pi}\sum_{p=2k}^{3k}(2|r|)^{(p+1)/2}C_{k,p}\modBesselK{2\ell+1+p}@{\sqrt{8|r|}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r < 0} | H[k](ell ; r) = (- 1)^(ell + 1)*(2)/(Pi)*sum((2*abs(r))^((p + 1)/2)* C[k , p]*BesselK(2*ell + 1 + p, sqrt(8*abs(r))), p = 2*k..3*k)
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Subscript[H, k][\[ScriptL]; r] == (- 1)^(\[ScriptL]+ 1)*Divide[2,Pi]*Sum[(2*Abs[r])^((p + 1)/2)* Subscript[C, k , p]*BesselK[2*\[ScriptL]+ 1 + p, Sqrt[8*Abs[r]]], {p, 2*k, 3*k}, GenerateConditions->None]
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Translation Error | Translation Error | - | - |