梅西纳-珀拉泽克多项式维基百科,自由的 encyclopedia 梅西纳-珀拉泽克多项式是一个以超几何函数定义的正交多项式 P n ( λ ) ( x ; ϕ ) = ( 2 λ ) n n ! e i n ϕ 2 F 1 ( − n , λ + i x ; 2 λ ; 1 − e − 2 i ϕ ) {\displaystyle P_{n}^{(\lambda )}(x;\phi )={\frac {(2\lambda )_{n}}{n!}}e^{in\phi }{}_{2}F_{1}(-n,\lambda +ix;2\lambda ;1-e^{-2i\phi })} P n λ ( cos ϕ ; a , b ) = ( 2 λ ) n n ! e i n ϕ 2 F 1 ( − n , λ + i ( a cos ϕ + b ) / sin ϕ ; 2 λ ; 1 − e − 2 i ϕ ) {\displaystyle P_{n}^{\lambda }(\cos \phi ;a,b)={\frac {(2\lambda )_{n}}{n!}}e^{in\phi }{}_{2}F_{1}(-n,\lambda +i(a\cos \phi +b)/\sin \phi ;2\lambda ;1-e^{-2i\phi })} Meixner-Pollaczek Polynomials animation Meixner-Pollaczek Polynomials animation
梅西纳-珀拉泽克多项式是一个以超几何函数定义的正交多项式 P n ( λ ) ( x ; ϕ ) = ( 2 λ ) n n ! e i n ϕ 2 F 1 ( − n , λ + i x ; 2 λ ; 1 − e − 2 i ϕ ) {\displaystyle P_{n}^{(\lambda )}(x;\phi )={\frac {(2\lambda )_{n}}{n!}}e^{in\phi }{}_{2}F_{1}(-n,\lambda +ix;2\lambda ;1-e^{-2i\phi })} P n λ ( cos ϕ ; a , b ) = ( 2 λ ) n n ! e i n ϕ 2 F 1 ( − n , λ + i ( a cos ϕ + b ) / sin ϕ ; 2 λ ; 1 − e − 2 i ϕ ) {\displaystyle P_{n}^{\lambda }(\cos \phi ;a,b)={\frac {(2\lambda )_{n}}{n!}}e^{in\phi }{}_{2}F_{1}(-n,\lambda +i(a\cos \phi +b)/\sin \phi ;2\lambda ;1-e^{-2i\phi })} Meixner-Pollaczek Polynomials animation Meixner-Pollaczek Polynomials animation