Carotid-Kundalini function
卡咯提的-昆达利尼函数(Carotid-Kundalili Function)定义如下[1]
与其他特殊函数的关系[编辑]
![{\displaystyle 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))}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fdcd9033a7095f48c4e7226c4d0e192e3e9c1252)
![{\displaystyle K(n,x)={\frac {(nxcos^{1}(x)+\pi /2)KummerM(1,2,I(2nxarccos(x)+\pi ))}{exp(I(2nxarccos(x)+2\pi /2))}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb72e33d298217697ab93aaddd7196d62c62817c)
![{\displaystyle -n{x}^{2}{\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){\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa7fc46a3191320ed4f8dbd951ffcba5210ec3b0)
函数展开[编辑]
帕德近似[编辑]
帕德近似:
外部链接[编辑]
参考文献[编辑]
- ^ Weisstein, Eric W. "Carotid-Kundalini Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Carotid-KundaliniFunction.html (页面存档备份,存于互联网档案馆)