10.40: Difference between revisions

From testwiki
Jump to navigation Jump to search
VisualWikitext
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/10.40.E10 10.40.E10] || [[Item:Q3588|<math>\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)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <math>k \geq 1</math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Failure || Failure || Error || Error
| [https://dlmf.nist.gov/10.40.E10 10.40.E10] || <math qid="Q3588">\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)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)</syntaxhighlight> || <math>k \geq 1</math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Failure || Failure || Error || Error
|}
|}
</div>
</div>

Latest revision as of 11:26, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.40.E10 K ν ⁡ ( z ) = ( π 2 ⁢ z ) 1 2 ⁢ e - z ⁢ ( ∑ k = 0 ℓ - 1 a k ⁢ ( ν ) z k + R ℓ ⁢ ( ν , z ) ) modified-Bessel-second-kind 𝜈 𝑧 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 ℓ 1 subscript 𝑎 𝑘 𝜈 superscript 𝑧 𝑘 subscript 𝑅 ℓ 𝜈 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\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)		 k ≥ 1 𝑘 1 {\displaystyle{\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))

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])
Failure Failure Error Error
Retrieved from "https://lct.wmflabs.org/w/index.php?title=10.40&oldid=58210"