Bessel Functions - 10.40 Asymptotic Expansions for Large Argument
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 10.40.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right)}
\modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k \geq 1} | BesselK(nu, z) = ((Pi)/(2*z))^((1)/(2))* exp(- z)*(sum((((4*(nu)^(2)- (1)^(2))*(4*(nu)^(2)- (3)^(2)) .. (4*(nu)^(2)-(2*k - 1)^(2)))/(factorial(k)*(8)^(k)))/((z)^(k)), k = 0..ell - 1)+ R[ell](nu , z))
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BesselK[\[Nu], z] == (Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*(Sum[Divide[Divide[(4*\[Nu]^(2)- (1)^(2))*(4*\[Nu]^(2)- (3)^(2)) \[Ellipsis](4*\[Nu]^(2)-(2*k - 1)^(2)),(k)!*(8)^(k)],(z)^(k)], {k, 0, \[ScriptL]- 1}, GenerateConditions->None]+ Subscript[R, \[ScriptL]][\[Nu], z])
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Failure | Failure | Error | Error |