Bessel Functions - 10.17 Asymptotic Expansions for Large Argument
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 10.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{|z|}+\tfrac{1}{2}i\phase@@{z}}}
z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{|z|}+\tfrac{1}{2}i\phase@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (z)^((1)/(2)) = exp((1)/(2)*ln(abs(z))+(1)/(2)*I*argument(z))
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(z)^(Divide[1,2]) == Exp[Divide[1,2]*Log[Abs[z]]+Divide[1,2]*I*Arg[z]]
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Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.17.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}}
\scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{p} > 0} | (exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z)
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Error
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Successful | Missing Macro Error | - | - |
| 10.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{+}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(+ i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{- 2iz}+R_{m,\ell}^{+}(\nu,z)\right)}
R_{\ell}^{+}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(+ i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{- 2iz}+R_{m,\ell}^{+}(\nu,z)\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\ell-k)} > 0, k \geq 1} | (R[ell])^(+)(nu , z) = (- 1)^(ell)* 2*cos(nu*Pi)*(sum((+ I)^(k)*(((4*(nu)^(2)- (1)^(2))*(4*(nu)^(2)- (3)^(2)) .. (4*(nu)^(2)-(2*k - 1)^(2)))/(factorial(k)*(8)^(k)))/((z)^(k))*(exp(- 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,- 2*I*z), k = 0..m - 1)+ (R[m , ell])^(+)(nu , z))
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Error
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Error | Missing Macro Error | - | - |
| 10.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{-}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(- i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{+ 2iz}+R_{m,\ell}^{-}(\nu,z)\right)}
R_{\ell}^{-}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(- i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{+ 2iz}+R_{m,\ell}^{-}(\nu,z)\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\ell-k)} > 0, k \geq 1} | (R[ell])^(-)(nu , z) = (- 1)^(ell)* 2*cos(nu*Pi)*(sum((- I)^(k)*(((4*(nu)^(2)- (1)^(2))*(4*(nu)^(2)- (3)^(2)) .. (4*(nu)^(2)-(2*k - 1)^(2)))/(factorial(k)*(8)^(k)))/((z)^(k))*(exp(+ 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,+ 2*I*z), k = 0..m - 1)+ (R[m , ell])^(-)(nu , z))
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Error
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Error | Missing Macro Error | - | - |