查看“︁卡咯提的-昆达利尼函数”︁的源代码

[[File:Carotid Fractal.png|thumb|right|Carotid-Kundalini function]]
'''卡咯提的-昆达利尼函数'''（Carotid-Kundalili Function）定义如下<ref>Weisstein, Eric W. "Carotid-Kundalini Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Carotid-KundaliniFunction.html {{Wayback|url=http://mathworld.wolfram.com/Carotid-KundaliniFunction.html |date=20191208091526 }}</ref>

<math>K(n, x)= cos(n*x*arccos(x))</math>

==与其他特殊函数的关系==
*<math> K(n,x)=\frac{ -(1/2*I)*(-1+exp(I*(2*n*x*arccos(x)+Pi)))}{exp((1/2*I)*(2*n*x*arccos(x)+Pi))} </math>
*<math> K(n,x)= \frac{(nxcos^1(x)+\pi/2)KummerM(1,2,I(2nxarccos(x)+\pi))}{exp(I(2nxarccos(x)+2\pi/2))} </math>

*<math>-n{x}^{2}{\it HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {1/2\,i \left( 2\,n
x \left( 1/2\,\pi -x{\it HeunC} \left( 0,1/2,0,0,1/4,{\frac {{x}^{2}}{
{x}^{2}-1}} \right) {\frac {1}{\sqrt {1-{x}^{2}}}} \right) +\pi 
 \right) } \right) {\it HeunC} \left( 0,1/2,0,0,1/4,{\frac {{x}^{2}}{{
x}^{2}-1}} \right) {\frac {1}{\sqrt {1-{x}^{2}}}} \left( {{\rm e}^{-1/
2\,i \left( -nx\pi \,\sqrt {1-{x}^{2}}+2\,n{x}^{2}{\it HeunC} \left( 0
,1/2,0,0,1/4,{\frac {{x}^{2}}{{x}^{2}-1}} \right) -\pi \,\sqrt {1-{x}^
{2}} \right) {\frac {1}{\sqrt {1-{x}^{2}}}}}} \right) ^{-1}+1/2\,\pi 
\, \left( nx+1 \right) {\it HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {1/2
\,i \left( 2\,nx \left( 1/2\,\pi -x{\it HeunC} \left( 0,1/2,0,0,1/4,{
\frac {{x}^{2}}{{x}^{2}-1}} \right) {\frac {1}{\sqrt {1-{x}^{2}}}}
 \right) +\pi  \right) } \right)  \left( {{\rm e}^{-1/2\,i \left( -nx
\pi \,\sqrt {1-{x}^{2}}+2\,n{x}^{2}{\it HeunC} \left( 0,1/2,0,0,1/4,{
\frac {{x}^{2}}{{x}^{2}-1}} \right) -\pi \,\sqrt {1-{x}^{2}} \right) {
\frac {1}{\sqrt {1-{x}^{2}}}}}} \right) ^{-1}
</math>

<math>K(n,x)={\frac {-i \left( 2\,nx\arccos \left( x \right) +\pi  \right) 
{{\rm \it WhittakerM}\left(0,\,1/2,\,i \left( 2\,nx\arccos \left( x \right) +\pi  \right) \right)}
}{4\,nx\arccos \left( x \right) +2\,\pi }}


</math>

==函数展开==
<math>K(n,x) \approx  {1-(1/8)*n^2*\pi^2*x^2+(1/2)*n^2*\pi*x^3+((1/384)*n^4*\pi^4-(1/2)*n^2)*x^4+(-(1/48)*n^4*\pi^3+(1/12)*n^2*\pi)*x^5+O(x^6)}</math>
==帕德近似==
[[帕德近似]]:

<math>K(n,x) \approx  \left\{ {\frac { 1800.0+ \left( - 36.4\,{n}^{4}+ 516.0 \right) x+
 \left( - 46.3\,{n}^{4}- 1830.0\,{n}^{2}- 71.0 \right) {x}^{2}+
 \left(  1820.0\,{n}^{2}+ 37.4\,{n}^{6}- 44.3\,{n}^{4}+ 81.9 \right) {
x}^{3}}{ 1800.0+ \left( - 36.4\,{n}^{4}+ 516.0 \right) x+ \left( -
 46.3\,{n}^{4}+ 368.0\,{n}^{2}- 71.0 \right) {x}^{2}+ \left( - 7.48\,{
n}^{6}- 44.3\,{n}^{4}- 363.0\,{n}^{2}+ 81.9 \right) {x}^{3}}}
 \right\} 
</math>
==外部链接==
*[http://smallsats.org/2014/01/03/carotid-kundalini-function/ Carotid-Kundalini function] {{Wayback|url=http://smallsats.org/2014/01/03/carotid-kundalini-function/ |date=20201127175232 }}

==参考文献==
<references/>

[[Category:特殊函数]]