惠泰克函数维基百科,自由的 encyclopedia 惠泰克函数,惠泰克1904推导合流超几何函数,是下列惠泰克方程的解[1] d 2 w d z 2 + ( − 1 4 + κ z + 1 / 4 − μ 2 z 2 ) w = 0. {\displaystyle {\frac {d^{2}w}{dz^{2}}}+\left(-{\frac {1}{4}}+{\frac {\kappa }{z}}+{\frac {1/4-\mu ^{2}}{z^{2}}}\right)w=0.} WhittakerM function Whittaker W function 此方程在 0 有用正则奇点,在 ∞ 有非正则奇点. 惠泰克方程有两个解[2] M 与 U : M κ , μ ( z ) = exp ( − z / 2 ) z μ + 1 2 M ( μ − κ + 1 2 , 1 + 2 μ ; z ) {\displaystyle M_{\kappa ,\mu }\left(z\right)=\exp \left(-z/2\right)z^{\mu +{\tfrac {1}{2}}}M\left(\mu -\kappa +{\frac {1}{2}},1+2\mu ;z\right)} W κ , μ ( z ) = exp ( − z / 2 ) z μ + 1 2 U ( μ − κ + 1 2 , 1 + 2 μ ; z ) . {\displaystyle W_{\kappa ,\mu }\left(z\right)=\exp \left(-z/2\right)z^{\mu +{\tfrac {1}{2}}}U\left(\mu -\kappa +{\frac {1}{2}},1+2\mu ;z\right).}
惠泰克函数,惠泰克1904推导合流超几何函数,是下列惠泰克方程的解[1] d 2 w d z 2 + ( − 1 4 + κ z + 1 / 4 − μ 2 z 2 ) w = 0. {\displaystyle {\frac {d^{2}w}{dz^{2}}}+\left(-{\frac {1}{4}}+{\frac {\kappa }{z}}+{\frac {1/4-\mu ^{2}}{z^{2}}}\right)w=0.} WhittakerM function Whittaker W function 此方程在 0 有用正则奇点,在 ∞ 有非正则奇点. 惠泰克方程有两个解[2] M 与 U : M κ , μ ( z ) = exp ( − z / 2 ) z μ + 1 2 M ( μ − κ + 1 2 , 1 + 2 μ ; z ) {\displaystyle M_{\kappa ,\mu }\left(z\right)=\exp \left(-z/2\right)z^{\mu +{\tfrac {1}{2}}}M\left(\mu -\kappa +{\frac {1}{2}},1+2\mu ;z\right)} W κ , μ ( z ) = exp ( − z / 2 ) z μ + 1 2 U ( μ − κ + 1 2 , 1 + 2 μ ; z ) . {\displaystyle W_{\kappa ,\mu }\left(z\right)=\exp \left(-z/2\right)z^{\mu +{\tfrac {1}{2}}}U\left(\mu -\kappa +{\frac {1}{2}},1+2\mu ;z\right).}